Page 1
A≤ymbw 22 (Bbp¿±mbZiIƒ) 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Language : Malayalam
PHALADEEPIKA (INDIAN ASTROLOGY)
CHAPTER TWENTY TWODIFFERENT SYSTEMS
FOR DETERMINING LONGEVITY
AUTHORMANTRESWARA
Translation, DTP and Layout by Mullappilly Protected with Copy Right Rules by the TranslatorotecteL
Page 2
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A≤ymbw 22 (Bbp¿±mbZiIƒ) 465
A≤ymbw 22
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Page 4
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ImeN{IZi (t«mIw 1˛15), D¬∏∂mZm\almZiIƒ (t«mIw 16), \nk¿§Zi (17),
AwiIZi (t«mIw 18˛20), D®\oNZi (t«mIw 21˛24), Pohi¿ΩobZi (t«mIw 25)
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2 ImeN{IZi ImWp∂ hn[w: :
1. BZyambn P\\kabsØ \£{X]mZw ImWpI.
2. \£{X]mZwsh®v P\\kabsØ cminZi ImWpI.
cmin\mY≥Xs∂bmWv Zim\mY≥.
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Page 5
A≤ymbw 22 (Bbp¿±mbZiIƒ) 467
(1)
Z{kmZnXx ]mZhti\ tajm˛
∑o\mwiIm¥w {Iatim f ]khyw (1)
IoSm≤bm¥w KWtb® khy˛
am¿tKW(2) ]mZ{Iatim f PXmcm¬.
]mTt`Zw : (1) {IatimY Z£X
(2) hmaam¿t§W
3. \£{X]mZßfn¬ cminZiIfpsS hn\ymkw( tajmXv ao\mwiIm¥hpw IoSm≤bm¥hpw )
1. A]khyw ˛ A]khyamb
Z{kmZnXx ˛ AizXn apXemb \£{XßfpsS
(AizXn, `mcWn, Im¿ØnI KWßfpsS)
]mZhti\ ˛ ]mZ߃°\pkrXambn.
tajmXv ao\mwiIm¥w {Iaix˛ taSw apX¬ ao\whscbp≈ cminIƒ
{IaØnepw
IoSm≤bm¥w --̨ hr›nIw apX¬°p [\phscbp≈ cminIƒ
]ndtIm´pw F∂ {IaØn¬
KWtbXv N ˛ ZiIƒ KWn°Ww.
2. khyam¿tKW ˛ khyamb
APXmcm¬ ˛ tcmlnWn apXemb \£{XßfpsS ImcyØnepw
(tcmlnWn, aIbncw, XncphmXnc KW߃)
. ]mZ{Iatim - ˛ ------Cßs\ ]mZ{IaØn¬ ZiIƒ KWn°Ww.
(AhnsS cminIfpsS {Iaw CXn\p hn]coXamWv.)
Hcp \£{XØn\v \mep ]mZ߃. Hcp ]mZØn\v HºXp ZiIƒ. CXp {]Imcw Hcp
\£{XØn\v 36 ZiIƒ hcpw. 36 ZiIƒ h´saØm≥ ]{¥≠p cminIƒ aq∂p h´w
Bh¿Øn®p hcWw. CXn¬ BZysØ ]{¥s≠Æw taSw apX¬ ao\w hsc F∂p
km[mcW{IaØnepw ]ns∂ ]{¥s≠Æw hr›nIw apX¬ -- [\phsc F∂p hn]coX
{IaØnepw ASpØ ]{¥s≠Æw taSw apX¬ ao\w hsc F∂ km[mcW {IaØnepw
Bh¿Øn®phcpw.
(CXp hy‡ambn a\ nemIm≥ t«mI߃ 5˛9 IqSn ImWWw).
Page 6
^eZo]nI 468
4. A]khy khy\£{X߃( Z{kmZnX.....APXmcmXv )
A]khyw (heXv) khyw (CSXv)
(2)
Ghw `qbm®m]khyw N khyw
`m\n {XoWn ({XoWn) hnZymXv{ItaW
X{Zmioit{]m‡h¿ssj¿Zim kym˛
tZhw {]mlpx ImeNt{I alm¥x.
Ghw `qbmXv N A]khyw N khyw ... ˛ C{]Imcw A]khyhpw khyhpamb
\£{X߃
`m\n {XoWn ({XoWn) hnZymXv{ItaW... (ta¬∏d™Xpt]mse) apΩq∂p hoXap≈
\£{XKWßfmIp∂p
XXv cmioi t{]m‡ h¿ssj Zim kymXv˛ (AhbpsS ]mZ߃°\pkcn®p hcp∂)
cmin\mY∑m¿°p ]d™n´p≈XmIp∂p
AhbpsS Zimh¿j߃.
apIfn¬ ]d™ Bdp \£{XKWfn¬ AizXn, `cWn, Im¿ØnIbpw Ahbv°p
Xmsgbp≈hbpw Hcp hn`mKhpw (A]khyw) tcmlnWn, aIbncw, XncphmXncbpw
Ahbv°p Xmsgbp≈hbpw as‰mcp hn`mKhpw (khyw) BWv. F∂m¬, \£{XKW߃
BsdÆaps≠¶nepw ImeN{IZibn¬ AizXn, `cWn, tcmlnWn, aIbncw F∂nßs\
\mep KW߃t° cminZimhn\ymkw hcp∂p≈p. (C°mcyw t«mIw Ggn¬
hy‡am°p∂p≠v.) AXpsIm≠v, Hcp \£{XØn\v \mep ]mZ߃ sh®v 27
\£{X߃°v 108 ]mZßfps≠¶nepw ChnsS ZibpsS ImcyØn¬ 4 KWw $ 4 ]mZw =
16 ]mZßtf ]cnKWn°p∂p≈p. F∂m¬ Cu 16 ]mZ߃°pw HºXphoXw {KlßfpsS
Zi hcp∂p≠v. AXns‚ {Iahpw {KlßfpsS Zimh¿jhpamWv C\n ]dbp∂Xv.
(3)
a\px ]cx k\n¿[\n¿\r]kvXt]m ht\ {IamXv
ZnhmIcmZn h’cmx ip`mip`m]vXntlXhx.
(1) (2) (3) (4) (5) (6)
1. AizXn 2. `cWn 3. Im¿ØnI 4.tcmlnWn 5.aIbncw 6.XncphmXnc
7. ]pW¿Xw 8. ]qbw 9. Bbneyw 10. aIw 11. ]qcw 12. D{Xw
13. AØw 14. Nn{X 15. tNmXn 16. hnimJw 17.A\ngw 18. Xrt°´
19. aqew 20. ]qcmSw 21. D{XmSw 22.Xn.thmWw 23. Ahn´w 24. NXbw
25. ]qcqcp´mXn 26. D{X´mXn 27. tchXn
Page 7
A≤ymbw 22 (Bbp¿±mbZiIƒ) 4695. ImeN{IZibn¬ {KlßfpsS Zimh¿j߃
cmin Nnßw I¿°Sw taSw& anYp\w& [\p& CShw& aIcw&
hr›nIw I∂n ao\w Xpemw Ipw`w
cmiym[n] c N Ip _p Kp ip a
a\p ]c k\n [\n \r] X] h\
50 12 70 09 01 61 40
5 21 7 9 10 16 4
{IamXv ˛ Cßs\ {IaØn¬ --
ZnhmIcmZn h’cmx ˛ kqcy≥ XpSßnbhcpsS Zimh¿jw BIp∂p.
ip`mip`m]vXntlXhx ˛ (Ah) ip`hpw Aip`hpw Bb ^e߃°v
tlXphmIp∂p.
(IS-]-bmZn A£-c-kwJy A\p_‘ambn sISpØn´p≠v.)
(4)
Zim]lmcmZnIImeNt{I
hmIym\n Z{kmZn]ZmZnPm\n
h£yman h¿ssÆ¿∂h`n¿`amss\˛
cmioih¿ssjx ]cambpc{X.
Z{kmZn ]ZmZnPm\n ˛ AizXn apXemb \£{XßfpsS ]mZßfpsS.
Zim]lmcmZnI cminNt{I ˛ ImeN{IZibnse ZiIfpw A]lmcßfpw.
hmIym\n ˛ hm°pIfn¬,
h¿ssÆ \h`nx ˛ HºXp h¿Æßfn¬, A£ckwJyIfn¬.
h£yman ˛ Rm≥ ]dbp∂p.
AizXn XpSßnb \£{XßfpsS ]mZ߃°v \n›bn®n´p≈ HºXp hoXap≈
cminIsf Rm≥ IS]bmZn A£ckwJyIfn¬ hnhcn°p∂p.
\mep \£{XKW߃. Hmtcm∂n\pw \mep ]mZ߃. Hcp ]mZØns‚ Iogn¬ 9
cminIƒ. AXmbXv Hcp \£{XKWØn\v BsI 36 cminIƒ thWw. CXp icnbm°m≥
taSwapX¬°v ao\whscbp≈ ]{¥≠p cminIƒ aq∂ph´w Bh¿Øn®p hcWw. Cu
Bh¿Ø\w c≠p hn[ØnemWv. BZyw taSwapX¬ ao\w hsc {IaØn¬. ]n∂oSv hr›nIw
apX¬ [\phsc ]ndtIm´v. (cminIƒ : 1 ˛ taSw, 2 CShw F∂ {IaØn¬)
(5)
]ucw Kmthm anX kwZnKv[w \£t{Xμpx k Xp `qiqew
cqt]{X£∂n[tbmcwtK hmWo Nÿw Z[n\£{X
Page 8
^eZo]nI 470
(6)
ZmkXthtim Kuco]p{Xw £∂n[nImtcm tKm`qtijw
kuZ[n\£t{Xlmkt¥m `uaKpcpx ]p{Xmt£m\m[n.
6. \£{X{Kq∏pIfpsS ImeN{IZim{Iaw A£ckwJyIfn¬ --
(1, 2) AizXn , Im¿ØnI KW߃
]u cw Km thm an X kw Zn Kv[w
]mZw 1 1 2 3 4 5 6 7 8 9
\ £ t{X μp k Xp `q iq ew
]mZw 2 10 11 12 8 7 6 4* 5 3
cq t] {X £ ∂n [ tbm cw tK
]mZw 3 2 1 12 11 10 9 1 2 3
hm Wo N ÿw Z [n \ £ {Xw
]mZw 4 4 5 6 7 8 9 10 11 12
(3) `cWn KWw
Zm k X th tim Ku co ]p {X
]mZw 1 8 7 6 4 5 3 2 1 12
£ ∂n [n Im tcm tKm `q ti jw
]mZw 2 11 10 9 1 2 3 4 5 6
k Z [n \ £ t{X lm k t¥m
]mZw 3 7 8 9 10 11 12 8 7 6
`u a Kp cp ]p {Xm t£m \m [n.
]mZw 4 4 5 3 2 1 12 11 10 9
(7)
hmIymt\yXm\yiznbmay¿£tbm¿tbm˛
\yizn\ymZym\y·n`kym]kthy
kthyftPtμzm¿h£yamtWjp hmtIy˛
jzntμm¿hmIymt\yh cu{Zky `qbx.
1. hmIym\n GXm\n ˛ Cu hmIy߃.
Aiznbman E£tbm ˛ AizXn, `cWn \£{XßfpsS
Page 9
A≤ymbw 22 (Bbp¿±mbZiIƒ) 471
(AizXn˛`cWn {Kq∏pIfpsS) \mep ]mZß
fpsS cminIƒ (Zim{Iaw) BIp∂p.
2 Aizn\ymZym\n A·n`ky A]kthy˛ A]khy\£{Xßfn¬AizXn XpSßnbh
bpsS (AizXn{Kq∏ns‚) hmIy߃ Xs∂
bmWv Im¿ØnI {Kq∏nt‚Xpw.
2. kthy AtPtμzm ˛ khy\£{Xßfn¬ tcmlnWn, aIbnc
\£{X߃°p
(tcmlnWn˛aIbnc{Kq∏pIƒ°p)
h£yamtWjp hmtIyjp ˛ C\n ]dbm≥ t]mIp∂ hmIyßfn¬
Ctμm hmIym\n Gh ˛ aIbncØns‚ hmIy߃Xs∂
cu{Zky `pb ˛ XncphmXncbv°pw hcp∂p.
tcmlnWn, aIbncw {Kq∏pIfpsS ]mZßfpsS cminIƒ Xmsg ]dbp∂p.. CXn¬
aIbncw{Kq∏n\pw XncphmXnc{Kq∏n\pw Htc hmIy߃Xs∂bmIp∂p.
(8)
t[\px t£t{X ]pctKm ip`p˛
kvXmkmw P{Xp £∂n[n Zmko
N¿amt`mKo cmb[n\m£˛
kv{Xn ]ucmwtKm inhXo¿∞m_vtP.
(4) tcmlnWn KWw
t[ \px t£ t{X ]p c tKm iw `p
]mZw 1 9 10 11 12 1 2 3 5 4
kvXm kmw P {Xp £ ∂n [n Zm ko
]mZw 2 6 7 8 12 11 10 9 8 7
N¿ am t`m Ko cm b [n \m £
]mZw 3 6 5 4 3 2 1 9 10 11
kv{Xn ]u cmw tKm in h Xo¿ ∞m _vtP.
]mZw 4 12 1 2 3 5 4 6 7 8
(9)
{X£\n[n¿Zm kqNoiwt`m
Kucb[o \£{Xw ]mcw
Page 10
^eZo]nI 472
tKmioh Xo¿tY Zm{Xo£˛
t∂m [olknXmwip¿t`mKo caym.
(5, 6) aIbncw, XncphmXnc KW߃
{X £ \n [n¿ Zm kq Noiw t`m
]mZw 1 12 11 10 9 8 7 6 5 4
Ku c b [o \ £ {Xw ]m cw
]mZw 2 3 2 1 9 10 11 12 1 2
tKm io h \o¿ tY Zm {Xn £ t∂m
]mZw 3 3 5 4 6 7 8 12 11 10
[o l kn Xmw ip¿ t`m Ko c aym.
]mZw 4 9 8 7 6 5 4 3 2 1
7. ImeN{IZibpsS ASnÿm\amb \£{X KW߃
(Npcp°Øn¬ --)
(1 (2) (3) (4)
AizXn `cWn tcmlnWn aIbncw
Im¿ØnI ]qbw aIw XncphmXnc
]pW¿Xw Nn{X hnimJw ]qcw
Bbneyw ]qcmSw XncpthmWw D{Xw
AØw D{X´mXn ˛ A\ngw
tNmXn ˛ ˛ XrtI´
aqew ˛ ˛ Ahn´w
D{XmSw ˛ ˛ NXbw
]qcpcp´mXn ˛ ˛ ˛
tchXn ˛ ˛ ˛
(10)
\£{X]mssZjyLSokap∞m
]q¿hm Zim XXv]Xnh¿jPmXm
]q¿thm‡]mZ{Iatim f {X hnZymXv
tIjmwNntZhw aXamlpcmcymx.
Page 11
A≤ymbw 22 (Bbp¿±mbZiIƒ) 473
\£{X]mssZ LSokap∞m ˛ P\\kabsØ \£{X]mZØnse \mgnI
sh®,v N{μ≥ \n¬°p∂ \£{X]mZØns‚
_m°n sh®v,
]q¿hm Zim XXv ]Xn h¿jPmXm ˛ BZysØ cminZi, injvSZi, B cmiym[n
]s‚ Zimh¿jØn¬ ImWWw.
]q¿thm‡]mZ{Iaix ˛ t\csØ ]d™ ]mZ{IaØn¬ XpS¿∂p≈
ZiIfpw ImWWw.
tIjm©ntZhw aXamlp Bcym ˛ CXmWv BNmcy∑mcpsS A`n{]mbw
8. injvSZi ImWp∂ coXnDZmlcWwPmXIw. tcmlnWn
\£{Xw tcmlnWn . \£{X KXw 47˛28 1/ 2 . \memw]mZw
\£{X]mZw: \memw]mZw
Zimcmin ao\w. Zim\mY≥ Kpcp. Zimh¿jw 10 h¿jw
{Inb
\£{XssZ¿Lyw 60 \mgnI. \£{XKXw 47˛281/
2
_m°n (60 ˛̨ 47 1/2) = 12˛311/2 _m°n
10 $ 12˛311/2 = 10 $ 12 $ 30 = 3600 $ 7515
15 15 $ 12 $ 30 $ 60 $10 = 8.35 h¿jw
4. 2 amkw
6 Znhkw
P\\injvSZi 8 h¿jw 4 amkw 6 Znhkw Qjm[n] KpcpZim.
\£{Xw 60 \mgnI F∂ IW°v CS°meØpsh®p amdnbXn\m¬ Ct∏mƒ Hmtcm
ZnhktØbpw \£{X\mgnI {]tXyIw t\mt°≠Xp≠v.]mcºcycoXnbnse
kabm[njvTnXamb KWnXØnte Cu _p≤nap´p≈p. ÿem[njvTnXamb B[p\nI
KWnXØn¬ N{μkv^pSwsh®v Cu {Inb Ffp∏w sNømw.
. DZmlcWw˛̨
N{μkv^pSw 1˛20˛33 = 50˛33
AXp hcp∂ \£{X]mZw = 50˛00 ˛̨ 53˛20 (tcmlnWn \memw ]mZw)
Zimcminbpw Zim\mY\pw = ao\w. Kpcp. 10 h¿jw
\£{X]mZØn¬ _m°n
53˛20 ˛̨ 50˛33 = 2˛473˛20 = 10
2˛47 ?
Page 12
^eZo]nI 474
10 $ 167 = 8.35 h¿jw = 8 h¿jw 4 amkw 6 Znhkw
200
Cu KWnXw IqSpX¬ Ffp∏Øn¬ sNøm≥ tS_nfpw e`yamWv.
XpS¿∂p≈ ZiIƒ ImWp∂ coXn
DZmlcWw
tcmlnWn {Kq∏v ]mZw 4
12 1 2 3 5* 4 6 7 8
ao\w taSw CShw anYp\w Nnß I¿°Sw I∂n Xpemw hr›nIw
Kp Ip ip _p c N _p ip Ip
8˛4˛6 7 16 9 5 21 9 16 7 ...........
(11)
Z{kmZn]mZ{]`rXo\n `m\mw
hmIym\n bm\y£c]w‡nPm\n
tXjmw {ItassWh Zim {]Iev]ym
hmIy{Iaw km[znXn tINnZmlpx
Z{kmZn]mZ{]`rXo\n `m\mw ˛ AizXn XpSßnb \£{XßfpsS ]mZ߃°p
hmIym\n bm\n A£c]w‡nPm\n ˛ A£ckwJyIfn¬ ]d™n´p≈
tXjmw {ItassWh Zim {]Iev]ym ˛ {IaØn¬ ZiIƒ ]dbWw.
hmIy{Iaw km[p CXn ˛ hmIy{IaamWv km[phmbn´p≈Xv F∂p
tINnZmlpx.. ˛ Nne¿ ]dbp∂p .
(12)
hmIy{Ita I¿Iyfnao\k‘u
afiqIKXyizhcπpXn›
knwlmhtemIkv{Xnhn[m XZm\ow
Zim¥cw ZpJ^e{]Zw kymXv.
9 Zim{IaØnse Nne {]tXyI cminKXnIƒ
(afiqI XpcK knwlmhtemI\ KXnIƒ)
hmIy{Ita ˛ hmIy{IaØn¬.
I¿°n Afn ao\ k‘u ˛ I¿°nSw, hr›nIw, ao\w ChIfpsS
k‘nIfn¬.(km[mcW A\ptema ˛{]Xn
temaKXnIƒ°p ]pdsa Zimcmin Iƒ°v)
afiqIKXn AizhcπpXn N knwlmhtemIx {Xnhn[m -
Page 13
A≤ymbw 22 (Bbp¿±mbZiIƒ) 475
˛ afiqIKXn, XpcKKXn, knwlmhtemI\w
F∂o aq∂p Xcw {]tXyI KXnIƒIqSn D≠v.
XZm\ow Zim¥cw ZpJ^e{]Zw kymXv ˛ AØcw ZiIƒ tZmj^ew sNøpw.
(1) knwlmhtemI\KXn
AizXn {Kq∏n¬, taSwapX¬ ao\whscbp≈ ]{¥≠p cminIfpsS Hcp ]cnhrØn
]q¿Ønbm°n, ASpØ ]{¥≠p cminIfpsS ]cnhrØn Bcw`n°p∂Xv hr›nI
ØnemWt√m. ao\Øn¬\n∂pw hr›nIØntebv°p ≈ Cu Nm´amWv knwlKXn. CXp
t]mse ]{¥≠p cminIfpsS Hcp ]cnhrØn ]q¿Ønbm°n ASpØXv Bcw`n°ptºm
sg√mw knwlKXn Bh¿Øn°p∂Xmbn ImWmw. knwlKXn˛̨
(1) knwlKXn.
\£{X{Kq∏v ]mZw ]mZw
AizXn 2 ao\w˛hr›nIw, 3 [\p˛taSw
`cWn 2 [\p˛taSw, 3 ao\w˛hr›nIw
tcmlnWn 2 hr›nIw˛ao\w. 3 taSw ˛[\p
aIbncw 2 taSw˛[\p, 3 hr›nIw˛ao\w
DZmlcWw
]mZw 2 10 11 12 8 7 6 4 5 3
]mZw 3 2 1 12 11 10 9 1 2 3
(2, 3) Aizhc (a¿°So) afiqI KXnIƒ
1. H‰ cminIƒ am{Xap≈ I¿°SI˛NnßßfnemWv Cu KXnIƒ hcp∂Xv.
2. AizXn˛`cWn {Kq∏pIfn¬ cmin{Iaw ]ndtIm´p t]mIptºmgpw
tcmlnWn˛aIbnc{Kq∏pIfn¬ apt∂m´v t]mIptºmgpamWv Cu c≠p
KXnIfp≠mhpI.
3. ImeN{IZibn¬ Zim{Iaw Hcp cminsb adnIS∂v (NmSn°S∂v) ASpØ
cminbntebv°p t]mIp∂XmWv afiqInZi.
4. Cßs\ NmSn°S∂ Zi ho≠pw ]ndtIm´p h∂p ]gb KXn XpScp∂XmWv
a¿°SoZi.
DZmlcWw cminIƒ
1. AizXn {Kq∏v ]mZw 2 6˛4˛5
2. `cWn {Kq∏v ]mZw 1 6˛4˛5
3. tcmlnWn{Kq∏v]mZw 1 3˛5˛4
]mZw 4 3˛5˛4
4. aIbncw {Kq∏v]mZw 3 3˛5˛4
Page 14
^eZo]nI 476
--sImSpß√p¿ ]Xn∏n¬ Cu aq∂p {]tXyI KXnIsf hnhcn°p∂ c≠p t«mI߃
ImWp∂p≠.v. XmXv]cyw CXpXs∂.
(13)
XZzmIyh¿W{Iatim f ]lmc˛
h¿jmltX XXv]cambpcm]vtX
XZm Zimbma]lmch¿j
kwJym› amkmμnhkm≥ htZbpx.
10. A]lmc߃ ImWp∂ coXnZimh¿jsØ A]lmc\mYs‚ h¿jwsIm≠p KpWn®v ]cambp psIm≠p
lcn®m¬ -- A]lmcImew In´pw.h¿jw Ign™p hcp∂Xns\ ]{¥≠psIm≠p
s]cp°nbm¬ amkhpw, amkw Ign™phcp∂Xns\ ap∏XpsIm≠p s]cp°nbm¬
Znhkhpw In´pw. ]cambp ns\∏‰n ]dbp∂Xv ASpØ t«mIØnemWv.
(14)
hmtIyjp bmhOcZmw {]amWw
hZ¥n XmhXv ]cambpc{X
tajmZ\oIw aZ\w KtP\
Xpμx ]p\ss›hapZocnXw XXv.
11. \£{X]mZ ]cambp vhmtIyjp.... ̨ (Xmsg) hmIyßfn¬ {]amWambn ]d™n´p≈ h¿jßfmWv Hmtcm
\£{X ]mZØns‚bpw ]cambp v.
tajmXv ˛ taSw XpSßnb cminIƒ°v
A\oIw aZ\w KtP\ Xpμx
001 58 38 68
= 100 85 83 86
Cu {Iaw AizXn, `cWn {Kq∏pIfptSXmWv.
]p\x N Ghw DZocnXw XXv ˛ tcmlnWn, aIbncw {Kq∏pIƒ°v CXp
hn]coXambn hcpw.
\£{X]mZw \£{X{Kq∏pIƒ \£{X{Kq∏pIƒ
AizXn˛`cWn tcmlnWn˛aIbncw
Im¿ØnI XncphmXnc
]mZw 1 100 86
Page 15
A≤ymbw 22 (Bbp¿±mbZiIƒ) 477
]mZw 2 85 83
]mZw 3 83 85
]mZw 4 86 100
Hcp \£{X]mZØns‚ Zimcw`w km[mcW KXnbn¬ -- cminIfpsS CSbv°mWp
hcpI. AXp ImcWw ]cambp v XnIbmsX hcpw. At∏mƒ ASpØ ]mZØns‚
Zim{IaØnse BZycminsb XpS¿® cminbmbn FSp°Ww. AtX \£{X]mZØns‚
cminIƒ Bh¿Øn®p hcpw F∂ A`n{]bhpw \nehnep≠v.
12 Zim^ew
(15)
almZimkp bXv^ew {]Io¿XnXw abm ]pcm
XtZh tbmPtbXv _pt[m Zimwkp ssNhamZnjp.
almZimkp ˛ hnwtimØcnZib°v (19, 20, 21 A≤ymbßfn¬)
bXv ^ew ˛ bmsXmcp ^eamtWm,
{]Io¿ØnXw abm ]pcm ˛ F∂m¬ t\csØ ]dbs∏´Xv,
XXv Gh ˛ AXpXs∂,
Zimwkp N Ghw BZnjp ˛ Cu ZiIƒ°pw,
tbmPtbXv ˛ tbmPn∏n®p ]dbWw.
ImeN{IZimk{ºZmbØnse Bbp¿KWnX`mKØns‚ Hcp kw{Klw am{XamWvv
ChnsS \¬Inbn´p≈Xv. hnkvXcn® ^e{]hN\Øn\v hnwtimØcnZibv°p ]d™
^e߃ tN¿Øp Nn¥n°mhp∂XmWv.
IqSpX¬ -- hnhc߃°pw hnkvXcn® ^e`mKØn\pw PmXI]mcnPmXw, {io
apØpkzmanbpsS ImeN{IZi XpSßnb {KŸßƒ klmbn°pw.
(ImeN{IZibnse Zim\mY]´nI A\n_‘w 4˛¬ sImSpØn´p≠v.)
2. DXv]∂ B[m\ almZiIƒ(\£{XZiIƒ)
(16)
P∑¿£mXv ]cXkvXp ]©a`hm f tYmXv]∂ kw⁄m Zim
kymZm[m\Zim f ]ytXm f jvSa`hmXv t£am∑lmJym Zim
Bkmtah Zimhkm\katb arXyp{]Zm kym∂rWmw
kz¬]m\¬]kambpjmw(1) {Xnh[]©¿t£ Zimbm¥nta.
(1) ]mTt`Zw ˛ km¬]w Zo¿Lkambpjmw
Page 16
^eZo]nI 4781. P∑¿£mXv ]cXkvXp ˛ P∑\£{XØn¬\n∂pw
]©a `hmXv D¬∏∂kw⁄m Zim ˛ A©masØ \£{XØns‚ Zi
D¬∏∂ F∂p t]cmb ZibmIp∂p.
2. B[m\Zim AjvSa`hmXv ˛ F´mw \£{XØns‚ Zi B[m\Zi.
3. t£amXv almJym Zim. ˛ t£aw ˛ kpJw ˛ \mev.
\memw \£{XØns‚ Zi almZi.
4. Zimhkm\katb arXyp{]Zx kymXv \rWmw
˛ Cu ZiIfpsS Ahkm\ kabw (Zimk‘n
Iƒ) a\pjy¿°p amcIamWv.
5. kz¬] A\¬] ka Bbpjmw ˛ A¬∏mbp v, Zo¿Lmbp v, a≤ymbp v
F∂nßs\bp≈ aq∂v Bbp¿KWØn¬
s∏´h¿°v
. {Xn h[ ]©¿t£ Zimbm¥nta. ˛ ({IaØn¬) aq∂v, Ggv, A©v F∂o \£{X
ßfpsS ZiIfpsS A¥yw arXyp{]ZamWv.
\£{X Bbp¿±iIƒ
\£{X߃ 5 8 4 3 7 5
t]cv D¬∏∂ B[m\ alm A¬∏ Zo¿L a≤y
3. \nk¿§Zi
(17)
GIw tZz \hhnwiXn¿[rXnIrXnx ]©mitZjmw {Iam˛
®{μmtcμpPip{IPohZn\Irss±hmIcoWmw kamx
sskz sskzx (1) ]pjvS^em \nk¿KP\nssXx ]w‡n¿Zimbmx {Iam˛
Zt¥ e·Zim ipt`Xn bh\m t\—¥n tINnØYm.
(1) ]mTt`Zw ˛ tkz tkz
GI tZz \h hnwiXnx [rXn IrXnx ]©miXv GXmx {IamXv
1 2 9 20 18 20 50 = (120) Cu {IaØn¬
N{μ Bc CμpP ip{I Poh Zn\IrXv ZnhmIcoWmw
N Ip _p ip Kp c a ˛ XpSßnbhcpsS
kamx ˛ (Zim) h¿j߃ BIp∂p.
Page 17
A≤ymbw 22 (Bbp¿±mbZiIƒ) 479
tkz tkz ]pjvS^em\n.... ˛ Zim\mY∑m¿°p _eaps≠¶n¬ Ah
chcpsS Zibn¬ ip`^e߃ D≠mIpw.
At¥y e·Zim ipt`Xn bh\m ˛ e·ZibpsS Ahkm\`mKw ip`sa∂mWv
bh\mNmcycpsS A`n{]mbw.
\ C—¥n tINnXv XYm ˛ Nne¿ CXnt\mSp tbmPn°p∂n√.
\nk¿§ZiIƒ
{Klw Zimh¿jw hb v (h¿jw)
N{μ≥ 1 1
IpP≥ 2 2˛3
_p[≥ 9 4˛12
ip{I≥ 20 13˛32
Kpcp 18 33˛50
chn 20 51˛70
aμ≥ 50 71˛120
e·Zi .... 5 Znhkw
BsI 120 h¿jw 5 Znhkw
\nk¿§Zimh¿jhpw Zim{Iahpw F√mh¿°pw Hcpt]msebmWv.
Cu Zimh¿j߃ ]q¿Æ_eap≈ AYhm ]ctam®∑mcmb {Kl߃°p≈XmWv.
AXp{]Imcw {Klw \oNØnemsW¶n¬ Zimh¿jw CXns‚ ]IpXntb hcq. Nne Ipdbv°
epIƒ (lcW߃) IqSn sNøm\p≠v. AXp sNbvXm¬ Pohi¿ΩZit]mse hcpw.
e·Øn¬ IpP≥ \n∂m¬ apgph≥ Bbp pw t]mIpw. N{μ≥ \n∂m¬ ]Ønsem∂p
t]mIpw.
Zn√n ]Xn∏pIfn¬ ChnsS sNdnb hyXymkw ImWp∂p≠v. e·Zi A¥yØn¬
ip`amIpsa∂Xn\p ]Icw i\nbpsS AºXp h¿jØn¬ e·Øns‚ ZiIqSn
Dƒs∏Sp∂psh∂ ImcyamWv bh\mNmcycpsS A`n{]mbambn sImSpØn´p≈Xv.
AsX¥mbmepw, a‰p ]e {KŸßfnepw CØcw ZiIfn¬ ˛̨ \nk¿§Zi, D®\oNZi
(]nfiZi), Pohi¿ΩobZi XpSßnbhIfn¬ ̨ ˛ {KlßfpsS Zimh¿jw ]dbp∂nSØv
e·Øns‚ Zimh¿jw ImWp∂ coXnIqSn sImSpØn´p≠v.
4. AwiIZiBbp¿±mbKWnXØnse Hcp {][m\ZibmWv AwiZi. hcmlanlnc≥ hfsc
_lpam\n®ncp∂ kXymNmcycptSXmWv Cu Zi. tlmcm imkv{XØn¬ Ggmw A≤ymb
Øn¬ (t«mIw 9 apX¬ 13 hsc) AwiIZi hnkvXcn®p ]dbp∂p≠v. kqcyN{μ∑mtc°mƒ
e·m[n]\p _eaps≠¶n¬ Cu ZimcoXnbmWp tbmPn°pI F∂mWv A`n{]mbw.
Page 18
^eZo]nI 480
(18)
en]vXoIrXy `tPXv {Klw JL\ss\kvX—njvSambpjvIem
BimJmiznlrXm_vZamkZnhkmx ktXymZntXw f imbpjn
h{InWyp®KtX {XnkwKpWanZw kzmwi{Xn`mtKmØta
ZznLv\w \oNKtX f ¿[a]yY Zfw autVy knXm¿°o hn\m.
1. AwiIZi ImWp∂ hn[w
1. en]vXoIrXy `tPXv {Klw JL\ss\kvX—njvSambpjvIem.....
ktXymZntX Awimbpjn ˛ kXymNmcy≥ ]d™ AwiIZibn¬
{Klw ˛ {Klkv^pSsØ.
en]vXoIrXy ˛ IeIfm°n.
`tPX v JL\ss\.
J L \ ss\
2 4 0 0 = 2400 sIm≠p lcn®m¬
XXv injvSambpjvIem ˛ In´p∂. injvSw (lcW^ea√, _m°n
hcp∂ kwJy) IeIfnep≈ Bbp mIp∂p
2 BimJmizn (BImimizn) lrXm_vZamkZnhkmx ktXymZntXw f imbpjn
˛ ta¬∏d™ IeIfnep≈ Bbp ns\
(1) 200 sIm≠p lcn®m¬ h¿jhpw
(2) _m°nsb 12 sIm≠p KpWn®v 200 sIm≠p lcn®m¬ amkhpw
(3) AXn¬ _m°n h∂Xns\ 30 sIm≠p KpWn®v 200sIm≠p lcn®m¬
Znhkhpw In´pw.
(Cßs\ F√m {KlßfptSbpw Bbp¿h¿jw ImWWw.)
tlmcbnse {Kl`p‡\hmwicminXpeyw.... F∂ hmIya\pkcn®v AwiIZibn¬
Hmtcm {Klhpw \¬Ip∂ Bb v B {Klw `pPn® (]n∂n´) \hmwiIØn\p XpeyamWv.
Hcp \hmwiØn\v Hcp h¿jw F∂XmWv IW°v. Hcp \hmwiw -= 3--̨ 20 = 200 ”.200 (\hmwiw) sIm≠pw 12 (cminN{Iw) sIm≠pap≈ c≠p lcWßsf tN¿ØmWv
^eZ]nIbn¬ 2400˛sIm≠p lcn°Wsa∂p ]d™ncn°p∂Xv. {Klkv^pSØn¬ F{X
\hmwißfp≠v F∂dnbm\mWv 200 sIm≠p lcn°p∂Xv.
Hcp \hmwiafiesØ AYhm AwiIN{IsØbmWv 12 kqNn∏n°p∂Xv.
H∂ne[nIap≈ afießsf IeIfnep≈ {Klkv̂ pSØn¬\n∂pw \o°m\mWv CXv.
AXns‚ Xm¬∏cyanXmWv. 200 IeIƒ hoXap≈ 12 AwiI߃ tNcptºmƒ Hcp afieamIpw.
(3˛20 $ 12 = 40 `mK). 360 `mKbp≈ cminN{IsØ HºXp `mKam°ptºmƒ 40 `mKbmWt√m
In´pI. AXmbXv, cminN{IsØ HºXnsem∂m°nbm¬ \hmwiafiew. \hmwiafie
sØ HºXnsem∂m°nbm¬ \hmwiw.
Page 19
A≤ymbw 22 (Bbp¿±mbZiIƒ) 481
{Klkv̂ pSsØ IeIfm°n, IeIsf 200 sIm≠p lcn®v, 12 -̨s‚ KpWnX߃ \o°w
sNbvXm¬, As√¶n¬ 2400˛sIm≠p lcn®m¬, In´p∂ injvSw IeIfnep≈ Bbp mWv.
CXns\ Hcp \hmwiØn\v Hcp h¿jw F∂ IW°n¬ h¿j˛amk˛Znhkßfm°Ww.
2 AwiIZi : KWnXwDZmlcWPmXIØnse kqcykv^pSw: = 1˛25˛31
1. {Klkv^pSsØ (1 cmin 25 `mK 31 Iesb) IeIfm°pI
1 $ 30 = 30 + 25 = 55 $ 60 = 3300 + 31 = 3331 Ie
2. AXnse 2400˛Iƒ F√mw \o°w sNbvXv injvSw ImWpI
3331˛s\ 2400 sIm≠p lcn°ptºmƒ 1 (2400) In´pw. CXns\
Dt]£n®v injvSwsIm≠v {Inb XpScWw. injvSw (3331 ˛̨ 2400 ) = 931 Ie
3. injvSw h∂ 931 Iesb Hcp \hmwiØn\v Hcp h¿jw F∂ IW°n¬
h¿jam°Ww
Hcp \hmwiw 3 `mK 20 Ie = 200 Ie
931 / 200 = 4.655 = 4 h¿jw
_m°n .655 s\ 12 sIm≠p s]cp°n amkßfm°Ww
(655 / 1000)$ 12 = 7.86 = 7 amkw
_m°n . 86 s\ 30 sIm≠p s]cp°n Znhkßfm°Ww
(86 / 100) $ 30 = 25.8 = 26 Znhkw
(.8 s\ 24 sIm≠p s]cp°n aWn°qtdm, 60 sIm≠p s]cp°n \mgnI
Itfm B°mw. ChnsS .5 t\°mƒ IqSpXembXn\m¬ 1 Bbn FSpØp.)
3. h{IØnepw D®Ønepw a‰pw \n¬°p∂ {KlßfpsS
Zimh¿jØn¬ hcp∂ h¿≤\
2. h{InWyp®KtX {XnkwKpWanZw kzmwi{Xn`mtKmØta ZznLv\w ....
h{InWyp®KtX...... ˛ h{IØntem D®Øntem D≈ {KlßfpsS
Bbp¿h¿jsØ.
{XnkwKpWanZw ˛ aq∂psIm≠p s]cp°Ww. (aq∂nc´nbm°Ww)
Page 20
^eZo]nI 482
kzmwi{Xn`mtKmØssax ZznLv\w ˛ kz¥w \hmwiw, kz¥w t{Z°mWw, h¿t§mØaw
Chbn¬ \n¬°p∂ {KlßfpsS Bbp¿
h¿jsØ c≠psIm≠p s]cp°Ww.
(Cc´nbm°Ww).
Zimh¿j h¿≤\˛̨
1. D®w, h{Iw $ 3 (+)
2. kzt£{Xw, kzt{Z°mWw,
kz\hmwiw, h¿t§mØa\hmwiw $ 2 (+)
4. \oNauVylcWw
3. \oNKtX f ¿[a]yY Zfw autVy knXm¿°o hn\m.\oNKtXx A¿≤....
\oNKtX f ¿[ ˛ \oNØnep≈ {KlØns‚ ]IpXn
Ipdbv°Ww.
Zfw autVy knX A¿°o hn\m. ˛ ip{I≥, i\n Chsbmgn®p≈ {Kl߃°v
auVyØn¬ ]IpXn Ipdbv°Ww.
\oNØnepw auVy Ønepw \n¬°p∂ {KlßfpsS Zimh¿jØn¬ hcp∂
Ipdhv˛̨
\oNw, auVyw (ip, a HgnsI) ˛ 1/2 (-- ˛̨ )
(19)
k¿hm¿≤{XnIrtXjp(1)j◊nXeh{lmtkm f kXmapXv{IamXv
cnx^mXv kXvkp Zfw XZm lcXn _teytIm _lptjzIt`
{Xywtim\w cn]pt` hn\m £nXnkpXw ktXym]tZti Zim˛
e·kymwikam _en\ypZbt` f kym{Xm]n Xpeym]n N..
(1) ]mTt`Zw: civanXehm{≤mtkm
5. Zriym¿≤lcWw.
1. cn^mXv ˛ 12 apXemb `mhßfn¬ \n¬°p∂
AkXm ˛ ]m]{KlßfpsS AwiIZibn¬ \n∂p
DXv{IamXv ˛ {IaØn¬
k¿hm¿≤{XnIrtXjpj◊nXeh{lmtkm
˛ apgph≥, ]IpXn, 1/3, 1/4, 1/5, 1/6 F∂
{IaØn¬ Bbp p Ipdbv°Ww.
2. kXvkp Zfw.... ˛ Cu`mhßfn¬ \n¬°p∂Xp ip`{Klßfm
Page 21
A≤ymbw 22 (Bbp¿±mbZiIƒ) 483
sW¶n¬ Cu ]d™Xns‚ ]IpXn hoXw
Ipd®m¬ aXn
3. _lpjp GIt` ˛ Hcp cminbn¬ ]e {Klßfps≠¶n¬
IqSpX¬ _eap≈ Hcp {KlØns‚ h¿j
Øn¬ am{Xta Ipdhp sNtø≠Xp≈q.
1. cnx^w apX¬°p≈ `mhßfn¬ (Zriym¿≤Øn¬) ]m]∑m¿ \n∂m¬
Bbp¿h¿jØn¬ hcp∂ Ipdhv
`mhw 12 11 10 9 8 7
Ipdbvt°≠Xv apgph≥ 1/2 1/3 1/4 1/5 1/6
2. Zriym¿≤Øn¬ ip`∑m¿ \n∂m¬ ]m]∑m¿°p ]d™Xn¬ ]IpXn Ipdbv°Ww
`mhw 12 11 10 9 8 7
Ipdhv 1/2 1/4 1/6 1/8 1/10 1/12
3. Hcp cminbn¬ H∂ne[nIw {Kl߃°p Zriym¿≤lcWw hcp∂psh¶n¬ IqSp
X¬ hcp∂Xv (lcWw A[nIap≈ Hcp {KlØns‚ Bbp n¬) am{Xta Ipdhp
hcptØ≠Xp≈p
6. i{Xpt£{XlcWw4. {Xywtim\w cn]pt` hn\m £nXnkpXw ˛ IpP≥ HgnsIbp≈ {Kl߃
i{Xpt£{XØn¬ \n∂m¬ 1/3 Ipdbv°Ww
.
AwiIZibnse samØw Iq´epw Ipdbv°epw:
1. h¿≤\Iƒ: D®w, h{Iw, kzt£{Xw, kzt{Z°mWw,
kz\hmwiw, h¿t§mØa\hmwiw
2. lcW߃: \oNlcWw, auVylcWw, Zriym¿≤lcWw i{Xpt£{XlcWw
Iq´epw Ipdbv°epw ˛ GXv BZyw thWw?
Cc´n°epIƒ BZyw sNøtWm, lcW߃ BZyw sNøtWm Fs∂mcp kwibw
hcmw. lcW߃ Ign®p _m°nbp≈Xns\ Cc´n°pIbm Wv th≠Xv. AXmbXv,
Zimh¿jw I≠v, \mep lcWßfpw sNbvXn´pthWw h{InWyp® KtX....bn¬ ]dbp∂
h¿≤\Iƒ sNøphm≥.
8. e·mbp v (AwiIZibnse e·Zi)5. e·kymwikamx ˛ e·Øn¬ sN∂ \hmwiØn\p XpeyamWv
e·mbp v,
Page 22
^eZo]nI 484
6. _en\n DZbt`... ˛ e·Øn\mWv A[nIw _esa¶n¬,
F{X cminbmtWm Ign™Xv, A{Xbpw
h¿jamWv e·mbp v. (Hcp \hmwiw Hcp
h¿jw / Hcp cmin Hcph¿jw)
1. e·cminsb°mƒ _ew e·cmiywiIØn\msW¶n¬ AwiIØn\p
Xpeyambncn°pw Bbp v. AYhm e·Øns‚ \hmwiIm[n]\v e·m[n]t\°mƒ _ew
IqSppsa¶n¬ e·kv^pSØn se cmin If™v _m°nsb IeIfm°n 200 sIm≠p
lcn°Ww. BZyw In´p∂Xp h¿jw. _m°nsb 12˛epw 30˛epw s]cp°n 200˛sIm≠p lcn®p
amkhpw Znhkhpw ImWWw.
2. AwiIØnt\°mƒ A[nIw _ew e·Øn\msW¶n¬ cmin°p X p e y a m W v
Bbp v. AYhm e·\hmwiIm[n]t\°mƒ e·m[n]\p _ew IqSpsa¶n¬
e·kv̂ pSsØ cminbS°w IeIfm°n (200 $ 9) 1800 sIm≠p lcn°Ww. lcW^ew
h¿jw. tijn®Xns\ amkhpw Znhkhpam°Ww. k]vX{KlßfptSbpw e·Øns‚bpw
ZiIƒ Hcpan®p Iq´nbXmWv AwiI Zibnse ]cambp v.
(20)
ktXym]tZix {]htcm f {X In¥p
Ip¿h¥ytbmKyw _lph¿§Wm`nx
BNmcyIw Xz{X _lpLv\Xmbm˛
taI¥p bZv̀ qcn XtZh Imcyw.
ktXym]tZix ˛ kXymNmcycpsS D]tZiw (a‰p≈hcptSX
t]£n®v)
{]hcx A{X ˛ {]hcamWv, t{ijvTamWv.
In¥p ˛ F∂m¬.
Ip¿h¥n AtbmKyw _lph¿§Wm`nx ˛ (F∂m¬ Nne¿) _lph¿§Ww ( series ofmultiplications) sIm≠v CXns\ AtbmKy
am°p∂p.
BNmcyIw Xp A{X ˛ ktXym]tZiw A\pkcn®v .
_lpLv\Xmbmw GI¥p bZv̀ qcn XXv Gh Imcyw
˛ ]e Iq´epIƒ hcp∂psh¶n¬ AXn¬ G‰hpw
A[nIap≈Xpam{Xw FSpØm¬ aXn.
Cu t«mIw tlmcmimkv{Xw Ggmw A≤ymbØn¬\n∂pap≈XmWv. (7-̨ -12) AhnsS
]nfiZi (D®\oNZi), Pohi¿ΩZi, AwiIZi F∂o aq∂v Bbp¿±mbZiIfpw
hnhcn®Xn\ptijamWv Cu t«mIw hcp∂Xv. a‰p c≠p ZiIsf At]£n®v AwiIZibmWv
IqSpX¬ IrXyambn ImWp∂Xv. F¶nepw Nne¿ KWnXw sX‰mbn sNbvXv AXns‚ KpWw
Page 23
A≤ymbw 22 (Bbp¿±mbZiIƒ) 485
Ifbp∂Xn\m¬ icnbmb coXn hy‡am°pIbmWv ChnsS.
Bbp¿±mbKWnXØn¬ kXymNmcys‚ Cu AwiIZiXs∂bmWv
t{ijvTambn´p≈Xv. ]t£, A\mhiyambv s]cp°epIƒsIm≠v Nne¿ AXns‚ KpWw
Ifbp∂p. AXmbXv, Hcp {Klw \n¬°p∂Xv Htc kabw AXns‚ kzt£{XØnepw
D®Ønepw h{IØnepw BsW¶n¬ Bbp¿±mbw BZyw Cc´n°pI, ]ns∂ aq∂nc´n B°pI,
F∂nßs\ ]e {InbIƒ sNøp∂p. Aßns\ ]mSn√. aq∂nc´nbm°pI F∂ H‰ {Inb
sNbvXm¬ aXn (IqSpX¬ KpWn°epIƒ hcptºmƒ G‰hpw A[nIap≈ Hcp KpW\w
am{Xw aXn F∂¿∞w.) Ipdbv°ens‚ ImcyØnepw Cu coXnX∂bmWv th≠Xv.
DZmlcWØn\v, i{Xpt£{XÿnXnbpw auVyhpw HØp hcp∂psh¶n¬ auVyØns‚Xp
am{Xw, AXmbXv ]IpXn am{Xw, Ipd®m¬ aXn.
5. ]nfiZi (D®\oNZi)
(21)
t[bw iqc itI {inbw kvab ]tc \n{Zmx kam `mkvIcmXv
]nfimJymbpjn ]q¿hh® lcWw k¿hw hnZ[ymZnl
et· ]m]n\n `w hnt\mZbessh¿\n¿≤m \XmMvssKx lrXw (1)
XymPyw kuay\nco£ntX¿f≤arWa{Xmbpjy`n⁄m hnZpx.
(1) ]mTt`Zw ˛ hnt\mZbessh¿hnLv\w \XmwtK lrXw.
1. ]nfiZimh¿j߃t[bw....]nfimJymbpjn ˛ kqcy≥ XpSßnbhcpsS ]nfimbp¿±mbw:
t[bw iqc itI {inbw kvab ]tc \n{Zmx kam `mkvIcmXv
91 52 51 21 51 12 02
19 25 15 12 15 21 20 ˛ ˛ F∂o h¿j߃ (127 h¿j߃)
c N Ip _p Kp ip a ˛ F∂ {IaØn¬
kqcymZn {Kl߃ \¬Ip∂, A\p{Iaambn´p≈, ]nfimbp h¿jßfmWv.
{Klw D®w h¿jw \oNw h¿jw
chn taSw 10 19 Xpemw 10 9 1/2
Nμ≥ CShw 3 25 hr›nIw 3 12 1/2
IpP≥ aIcw 28 15 I¿°SIw28 7 1/2
_p[≥ I∂n 15 12 ao\w 15 6
Kpcp I¿°Sw 5 15 aIcw 5 7 1/2
ip{I≥ ao\w 27 21 I ∂n 27 10 1/2
aμ≥ Xpemw 20 20 taSw 20 10
Page 24
^eZo]nI 486
2. lcW߃]q¿hhXv N lcWw k¿hw hnZ[ymZnl ˛ t\csØ AwiImbp¿±mb Øn\p ]d™
F√m lcWßfpw ]nfimbp¿±mbØnepw
sNøWw.
{Kl߃ AXyp®Øn¬ (kqcy≥ taSw 10T XpSßnbh) \n∂memWp ta¬{]d™
Zimh¿j߃ e`n°pI. CXn¬\n∂p hyXykvXambn \oNÿnXn, i{Xpt£{XÿnXn,
auVyw, Zriym¿≤ÿnXn, e·Øn¬ ]m]ÿnXn F∂o A©p kμ¿`ßfn¬
Zimh¿jßfn¬ am‰w hcpw. Chbn¬ \mep lcW߃ ˛̨ \oNlcWw, auVylcWw,
Zriym¿≤lcWw, i{Xpt£{XlcWw F∂nh ˛̨ Awimbp¿±mbØn\p ]d™Xpt]mse
Øs∂ sNøWw. A©matØXmb {IqtcmZblcWw C\n ]dbp∂p.
3. {IqtcmZblcWwet· ]m]n\n `w... ˛ e·Øn¬ ]m]{Kl߃ (c, Ip, a) \n¬°p∂p
s≠¶n¬˛̨
1. e·kv^pSØnse cminsb \o°n `mKIeIsf IeIfm°pI.
2. AXpsIm≠v Hmtcm {Klhpw \¬Ip∂ Bbp¿±mbh¿jsØ s]cp°pI
. AXns\(Aßns\ In´p∂ ^esØ)
3. \XmwtK lrXw ˛ \ X K ˛ 063 ˛ 360T sIm≠ v AYhm 360w x 60’ = 216000’sIm≠p) lcn°pI. lcW^ew e·Øn¬ \n¬°p∂ ]m]{KlØns‚ (Ie
Ifnep≈) lcWamWv.
4. CXns\ Htcm {Klhpw \¬Ip∂ Bbp n¬\n∂pw Ipd®m¬ IrXyamb
Zimh¿jw (ip≤mbp v ) In´pw.
kuay\nco£ntXm... ˛ e·Øn\p ip`ZrjvSnbps≠¶n¬ ]IpXn
Ipd®m¬ aXn.
(22)
e·Zimawikamw _ehXywti hZ¥n ss]fiymtJy
_ebp‡w bZn e·w cminkssahm{X (1) \mwtim∞m.
(1) ]mTt`Zw : Ztim‡m.
4. e·Zie·Zim ss]fimtJy ˛ ]nfimbp¿±mbØnse e·Zi
_ehXn Awti Awikamw ˛ e·Øns‚ AwiIw (e·\hmwiw)
_etØmSp IqSnbXmsW¶n¬ AwiI
Øn\p kam\amb h¿jw.
_ebp‡w bZn e·w cminkaw ˛ e·w _etØmSpIqSnbXmsW¶n¬ cmin°p
Xpeyamb h¿jw.
Page 25
A≤ymbw 22 (Bbp¿±mbZiIƒ) 487
1. e·Øns‚ \hmwi Im[n]\v e·m[n]t\°mƒ _ew IqSppsa¶n¬ e·kv^pS
Ønse cmin If™v _m°nsb IeIfm°n 200 sIm≠p lcn°Ww. BZyw In´p∂Xp
h¿jw. _m°nsb 12˛epw 30˛epw s]cp°n 200˛sIm≠p lcn®p amkhpw Znhkhpw
ImWWw.
2. e·m[n]\p e·\hmwiIm[n]t\°mƒ _ew IqSpsa¶n¬ e k v ^ p S s Ø
cminsb AS°w IeIfm°n 200 $ 9 = 1800 lcn°Ww. lcW^ew h¿jw. tijn®Xns\
amkhpw Znhkhpam°Ww.
3. cmiym[n]\pw \hmwiIm[n]\pw _ew Xpeyambn h∂m¬ c≠maXp ]d™ hn[w.)
(23)
lcWw \otN¿f≤arWw kymXv
kºq¿Æ t{]m‡h¿jap®Krtl
ss]fiymZu Zzy¥ctK
{]mss⁄kvss{XcminIw Nn¥yw.
5. \oNlcWw hy‡am°p∂plcWw \otN A¿≤w...
1. {Kl߃ D®ØnemsW¶nemWv ta¬∏d™ h¿j߃ In´pI.
2. {Kl߃ \oNØnemsW¶n¬ CXn¬ ]IpXn Ipdbpw.
3. D®Øn\pw \oNØn\pw CSbnepw \oNØn\pw D®Øn\pw CSbnepap≈
ÿnXn°v Bbp¿h¿jw ImWm≥ ss{XcminIw sNøWw .
(24)
ss]fiymJyambp¿{_phtX {][m\w
aWn∞NmWIyabmZb›
GX∂ km[znXyhZZv`Zt¥m (1)
hcmlkqcyky XtZh hmIyw.
(1) ]mTt`Zw: almt¥m ˛ alm∑m¿
6. A`n{]mbwss]fiymJyw Bbpx {_phtX {][m\w˛]nfimbp¿±mbw (D®\oNZi) DØa
amsWam∂mWv aWnŸ≥, NmWIy≥,
ab≥ F∂o BNmcy∑mcpsS
A`n{]mbw.
GXXv \ km[p CXn AhZXv `Zt¥m ˛ F∂m¬ Cu Zimk{ºZmbw Ip‰a‰X√
F∂p `Z¥≥ ]d™n´p≠v
hcmlkqcyky XtZh hmIyw ˛ hcmlanlncs‚ A`n{]mbhpw CXpXs∂
bmbncp∂p .
(`Z¥≥ ̨ _u≤k\ymkn / kXymNmcy≥).
Page 26
^eZo]nI 488
6. Pohi¿ΩZi
(25)
kqcymZnIm\mw kzatX\ Poh˛
i¿Ωm kzcmwiw ]cambptjm f {XAkym]n k¿hw lcWw hnt[bw
]q¿thm‡h√·Zima]ol.
1. kzatX\ Pohi¿Ωm ˛ Pohi¿Ω F∂ BNmcys‚ A`n{]mbØn¬
kqcymZnIm\mw ˛ kqcy≥ XpSßnb k]vX{KlßfpsS
Bbp¿±mbw
kzcmwiw ]cambpj A{X ˛ ]cambp ns\ Ggmbn `mKn®XmWv.
2. Akym]n k¿hw lcWw hnt[bw ˛ CXpw t\csØ ]d™ ˛̨ ]nfiZi
bv°p ]d™ ˛̨ F√m lcW߃°pw
hnt[bamWv.
3. ]q¿thm‡h√·Zima]ol ˛ e·Zibpw t\ctØ ]d™Xpt]mse ˛
˛ ]nfiZibv°p ]d™Xpt]mse ˛̨ Øs∂.
Cu ZimcoXnbn¬, \nk¿§ZibnteXpt]mse, ]cambp v 120 h¿jw 5 ZnhkamWv.
CXns\ Ggmbn `mKn®Xv ˛̨ 17 h¿jw 1 amkw 22 Znhkw ˛̨ BWv Hmtcm {KlØn‚bpw Zi.
17 h¿jw 1 amkw 22 Znhkw 8 \mgnI -34 hn\mgnI $ 7 = 120-̨ 5
]nfiZibv°p ]d™ F√m lcWßfpw CXn\pw thWw. e·Zibpw AXp t]mseØs∂.
7. ]pcpjmbp v F{X?
(26)
\rWmw ZzmZih’cm ZilXm Bbpx {]amWw ]ssc˛
cmJymXw ]caw iss\kv{Xn`KtWm bmh÷ss\cocnXw
tINn®{μkl{kZ¿i\anl t{]m‡w Ieu In¥p b˛
tZzmtZm‡w icZ»Xw ln ]cambp¿±mbamN£vatl.
1. \rWmw ZzmZih’cm ZilXm Bbpx {]amWw
˛ Nne hnZzm∑mcpsS A`n{]mbØn¬ a\pjycpsS Bbp v \q‰ncp]Xv
h¿jamWv
2. ]ssc BJymXw ]caw iss\x {Xn`KtWm bmhXv Pss\x CucnXw ˛
˛ F∂m¬ a‰p NnecpsS A`n{]mbØn¬ i\nbpsS aq∂p `KWImew
( 30 $ 3) BWv ]cambp v.
Page 27
A≤ymbw 22 (Bbp¿±mbZiIƒ) 489
3. tINnXv N{μkl{kZ¿i\anlt{]m‡w
˛ Bbncw ]q¿ÆN{μs\ ImWp∂XmWv ]q¿Æmbp v F∂pw ]£ap≠v.
4. Ieu In¥p bXv thtZm‡w icZ»Xw ln ]cambp¿±mbamN£vatl
˛ F∂m¬ thZw ]dbp∂Xv IenbpKØn¬ a\pjymbp v \qdp h¿jw
BsW∂mWv. \Ωfpw AXnt\mSp tbmPn°p∂p.
8. Zim{Iaw
(27)
e·mZntXyμpIm\ma[nI_ehXx
kym±imZu XtXm f \ym
XXvtI{μmZnÿnXm\manl _lpjp ]p\¿˛
hocytXm hocykmtay
_lzmbp¿h¿jZmXpx {]Yaan\him˛
t®mZnXkym_vZkmtay
hocyw InwXz{X k‘n¿{KlhnhclXw
`mhk‘y¥cm]vXw.
1. e· BZnXy Cμp`m\mw A[nI_ehXx kymXv ZimZu
˛ e·w, BZnXy≥, N{μ≥Chcn¬ A[nIw _eap≈ {KlØns‚ ZibmWv
BZyw hcpI.
2, XXx A\ym XXv tI{μmZn ÿnXm\mw Cl
˛ c≠maXmbn tI{μØn¬ \n¬°p∂ {KlØns‚ Zi hcpw
3. _lpjp ]p\x hocytXm
˛ tI{μØn¬ A[nIw {Kl߃ Ds≠¶n¬ Ahcn¬ _etadnbhs‚ Zi
FSp°Ww.
4. hocykmtay _lzmbpx h¿jZmXpx
˛ _ewsIm≠p XpeymhÿtbmSp IqSnb {Kl߃ tI{μØn¬ D≠mbm¬
A[nIw Bbp¿h¿jw Xcp∂ {KlØns‚ Zi FSp°Ww.
5. {]Yaw C\hti\ DZnX kymXv A_vZkmtay
˛ Bbp¿h¿jØnepw {Kl߃°p kmayw h∂m¬ kqcy_‘Øn¬\n∂pw
BZyw ]pdØp hcp∂ {KlØns‚ Zi BZyw hcpw.
6. hocyw Inw Xp A{X....
˛ C\n AYhm hocyw, Zimh¿jw, kqcytbmK Øn\ptijw BZyw DZn°pI
F∂nhsb√mØnepw HØphcnIbmsW¶n¬ ASpØ ÿm\Øp≈ {KlsØ
s°m≠p Nn¥n°Ww.
Page 28
^eZo]nI 490
9. Cu ZiIƒ Nn¥nt°≠sXt∏mƒ
(28)
Awtim¤hw e·_emXv{]km[y˛
ambp› ]ntfim¤ha¿°hocymXv
ss\k¿§nIw N{μ_emXv {]km[yw
{_qbmXv {XbmWma]n hocykmtay.
(29)
tXjmw {XbmWmanl kwbpXnkvXp
{Xn`n¿lrXm sskh Zim {]I¬]ym
hocyw ZztbmsscIyZfw Xtbmx kymXv
tN÷ohi¿ambpcao _tem\mx.
1. e·Øn\mWv _ew IqSpXse¶n¬ Awimbp pw
2. kqcy\mWp _esa¶n¬ ]nfimbp pw
3. N{μ\mWp _esa¶n¬ \nk¿§mbp pw FSp°Ww.
4. ap≥]d™ aq∂nepw _ekmayw hcpIbmsW¶n¬, aq∂phn[ Bbp pw
Hcpan®pIq´n aq∂psIm≠p lcn°Ww.
5 cs≠ÆØn\p Xpey_ew hcnIbmsW¶n¬ c≠pw XΩn¬ Iq´n
c≠psIm≠p lcn°pI.
6 aq∂n\pw _eans√¶n¬, Pohi¿ΩobcoXn A\pkcn®p Zi ImWpI.
(30)
ImeN{IZim t⁄bm N{μmwtiti _em\zntX
kZm \£{Xam¿t§W Zim _ehXo kvarXm.
1. N{μmwtiti _em\zntX ImeN{IZim t⁄bm
˛ N{μs‚ \hmwiØns‚ \mY\v _eaps≠¶n¬ ImeN{IZi A\pkcn®p
^ew AdnbWw.
2. \£{Xam¿t§W Zim kZm _ehXo kvarXm ˛̨ \£{XZi (hnwtimØcn) ˛̨
Ft∏mgpw, F√m kμ¿`ßfnepw, ^ew ImWn°p∂XmWv.
(31)
kamx jjvSn¿ZznLv\m a\pPIcnWmw ]© N \nim
lbm\mw Zzm{XnwiXv JcIc`tbmx ]©IIrXnx
hncq]m km Xzmbp¿hrjalnjtbm¿ZzmZi iq\mw
kvarXw OmKmZo\mw ZiIklnXmx jSv N ]caw.
Page 29
A≤ymbw 22 (Bbp¿±mbZiIƒ) 491
10. ]cambp v
1. jjvTn¿ZznLv\m a\pPIcnWmw... ˛ a\pjy¿°pw B\Iƒ°pw \q‰n bncp]Xp h¿jw
5 Znhkw
2. lbm\mw Zzm{XnwiXv ˛ IpXncbv°v ap∏Ønc≠p h¿jw
3. JcIc`tbmx ]©IIrXnx ˛ H´IØn\pw IgpXbv°pw Ccp]Ønb©p
h¿jw
4. hncq]m km]ymbpx hrjalnjtbm˛ Imfbv°pwt]mØn\pwCcp]Øn\mep h¿jw
5. ZzmZi iq\mw ˛ \mbbv°p ]{¥≠p h¿jw
6. OmKmZo\mw ZiIklnXmx jSv ˛ BSn\p ]Xn\mdp h¿jw
Cu t«mIw tlmcmimkv{XØn¬ --\n∂pap≈XmWv. (7˛5)
]cambpx h¿jw
h¿jw
a\pjy≥, B\ 120
IpXnc 32
H´Iw, IgpX 25
Imf, t]mØv 24
\mb 12
BSv 16
(32)
tb [¿ΩI¿Ω\ncXm hnPntX{μnbm›
tb]∞yt`mP\cXm ZznPtZh`‡mx
tb am\hm Z[Xn tb Ipeioekoamw
tXjmanZw IYnXambpcpZmc[o`nx.
11. ]cambp v B¿°p In´pw ?
1. tb [¿ΩI¿Ω\ncXm ˛ [¿ΩI¿Ωßfn¬ \ncXcmbn,
2. hnPntX{μnbm› - ˛ hnPntX{μnbcpambn
3. tb ]∞yt`mP\cXm ˛ ]∞y t`mP\Øn¬ cXcmbn
4. ZznPtZh`‡mx tb am\hm Z[Xn˛ {_m“WtZh`‡cmbn
5. tb Ipeioekoamw ˛ Ipeioe߃ A\pkcn®v Ignbp∂thm
tXjmanZw ˛ B a\pjy¿°mWv Cu Bbp v ]dbp∂Xv.
CXpw tlmcbnep≈ t«mIamWv. PmXI]mcnPmXhpw CXv D≤cn°p∂p≠v. .
Page 30
^eZo]nI 492
C∂sØ `mcXob^etPymXnjØns‚ ASnÿm\{KŸsa∂dnbs∏Sp∂
tlmcmimkv{Xw AYhm _rl÷mXIw hnhcn°p∂Xv D®\oNZi, Pohi¿ΩZi,
AwiIZi F∂o aq∂p Zimk{ºZmb߃ am{XamWv. Ah Bbp¿\n¿ÆbØn\p am{Xa√
s]mXphmb ^e{]hN\Øn\pw D]tbmKn°m≥ th≠ am¿§\n¿t±ißfpw AhnsS
\¬Ip∂p≠v. F∂m¬ GItZiw \m\qdp h¿j߃°p tijw kamlcn°s∏´
]cmictlmcbn¬ 28 ZiIsf∏‰n ]dbp∂p≠v. Chbn¬ hnwtimØcnbv°p sX°pw
AjvtSmØcnbv°p hS°pw C∂p IqSpX¬ -- {]Nmcap≠v. Bbp¿ \n¿ÆbØn\pw
km[mcWKXnbn¬ C∂v ChsbØs∂ B{ibn°p∂p.