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Language : Malayalam
PHALADEEPIKA
(INDIAN ASTROLOGY)
CHAPTER TWENTY TWO
DIFFERENT SYSTEMS
FOR DETERMINING LONGEVITY
AUTHOR
MANTRESWARA
Translation, DTP and Layout by Mullappilly
Protected with Copy Right Rules by the TranslatorotecteL
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t«mIßfpw. .Cu hnjbØn¬ PmXI]mcnPmXØn¬ ^e`mKhpw hniZmwißfpw AS°w
112 t«mIßfp≠v. Cu A≤ymbØnse hnjbw Bbp¿KWnXambXnm¬ AXnv
Bhiyamb KWnX`mKw am{Xta ^eZo]nIbpsS I¿Ømhv ChnsS hnhcn°p∂p≈q.
2 ImeN{IZi ImWp∂ hn[w: :
1. BZyambn PkabsØ £{X]mZw ImWpI.
2. £{X]mZwsh®v PkabsØ cminZi ImWpI.
cminmY≥Xs∂bmWv ZimmY≥.
144 ZiIfn¬ GXp ZibnemWv Pw hcp∂sX∂p ImWm≥ 3 apX¬ -- 7 hsc
t«mIßfn¬ -- Bhiyamb hnhc߃ Xcp∂p≠v. CXpsh®vv GXp cminZibn¬ BWv
Psa∂pw Zimh¿jw F{XbmsW∂pw Ffp∏Øn¬ Is≠Ømw.
A≤ymbw 22 (Bbp¿±mbZiIƒ) 467
(1)
Z{kmZnXx ]mZhti tajm˛
∑omwiIm¥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 hnymkw
( tajmXv aomwiIm¥hpw IoSm≤bm¥hpw )
1. A]khyw ˛ A]khyamb
Z{kmZnXx ˛ AizXn apXemb £{XßfpsS
(AizXn, `mcWn, Im¿ØnI KWßfpsS)
]mZhti ˛ ]mZ߃°pkrXambn.
tajmXv aomwiIm¥w {Iaix˛ taSw apX¬ aowhscbp≈ 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 CXnp hn]coXamWv.)
Hcp £{XØnv mep ]mZ߃. Hcp ]mZØnv HºXp ZiIƒ. CXp {]Imcw Hcp
£{XØnv 36 ZiIƒ hcpw. 36 ZiIƒ h´saØm≥ ]{¥≠p cminIƒ aq∂p h´w
Bh¿Øn®p hcWw. CXn¬ BZysØ ]{¥s≠Æw taSw apX¬ aow hsc F∂p
km[mcW{IaØnepw ]ns∂ ]{¥s≠Æw hr›nIw apX¬ -- [phsc F∂p hn]coX
{IaØnepw ASpØ ]{¥s≠Æw taSw apX¬ aow hsc F∂ km[mcW {IaØnepw
Bh¿Øn®phcpw.
(CXp hy‡ambn a nemIm≥ t«mI߃ 5˛9 IqSn ImWWw).
^eZo]nI 468
4. A]khy khy£{X߃
( Z{kmZnX.....APXmcmXv )
A]khyw (heXv) khyw (CSXv)
(2)
Ghw `qbm®m]khyw N khyw
`mn {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
`mn {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∂)
cminmY∑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° cminZimhnymkw hcp∂p≈p. (C°mcyw t«mIw Ggn¬
hy‡am°p∂p≠v.) AXpsIm≠v, Hcp £{XØnv 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 Cn ]dbp∂Xv.
(3)
apx ]cx kn¿[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.Angw 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
A≤ymbw 22 (Bbp¿±mbZiIƒ) 469
5. ImeN{IZibn¬ {KlßfpsS Zimh¿j߃
cmin Nnßw I¿°Sw taSw& anYpw& [p& CShw& aIcw&
hr›nIw I∂n aow Xpemw Ipw`w
cmiym[n] c N Ip _p Kp ip a
ap ]c kn [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 Ap_‘ambn sISpØn´p≠v.)
(4)
Zim]lmcmZnIImeNt{I
hmIymn Z{kmZn]ZmZnPmn
h£yman h¿ssÆ¿∂h`n¿`amss˛
cmioih¿ssjx ]cambpc{X.
Z{kmZn ]ZmZnPmn ˛ AizXn apXemb £{XßfpsS ]mZßfpsS.
Zim]lmcmZnI cminNt{I ˛ ImeN{IZibnse ZiIfpw A]lmcßfpw.
hmIymn ˛ 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∂npw mep ]mZ߃. Hcp ]mZØns‚ Iogn¬ 9
cminIƒ. AXmbXv Hcp £{XKWØnv BsI 36 cminIƒ thWw. CXp icnbm°m≥
taSwapX¬°v aowhscbp≈ ]{¥≠p cminIƒ aq∂ph´w Bh¿Øn®p hcWw. Cu
Bh¿Øw c≠p hn[ØnemWv. BZyw taSwapX¬ aow 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
^eZo]nI 470
(6)
ZmkXthtim Kuco]p{Xw £∂n[nImtcm tKm`qtijw
kuZ[n£t{Xlmkt¥m `uaKpcpx ]p{Xmt£mm[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)
hmIymtyXmyiznbmay¿£tbm¿tbm˛
yiznymZymy·n`kym]kthy
kthyftPtμzm¿h£yamtWjp hmtIy˛
jzntμm¿hmIymtyh cu{Zky `qbx.
1. hmIymn GXmn ˛ Cu hmIy߃.
Aiznbman E£tbm ˛ AizXn, `cWn £{XßfpsS
A≤ymbw 22 (Bbp¿±mbZiIƒ) 471
(AizXn˛`cWn {Kq∏pIfpsS) mep ]mZß
fpsS cminIƒ (Zim{Iaw) BIp∂p.
2 AiznymZymn 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 ˛ Cn ]dbm≥ t]mIp∂ hmIyßfn¬
Ctμm hmIymn Gh ˛ aIbncØns‚ hmIy߃Xs∂
cu{Zky `pb ˛ XncphmXncbv°pw hcp∂p.
tcmlnWn, aIbncw {Kq∏pIfpsS ]mZßfpsS cminIƒ Xmsg ]dbp∂p.. CXn¬
aIbncw{Kq∏npw XncphmXnc{Kq∏npw Htc hmIy߃Xs∂bmIp∂p.
(8)
t[px t£t{X ]pctKm ip`p˛
kvXmkmw P{Xp £∂n[n Zmko
N¿amt`mKo cmb[nm£˛
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
^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 ASnÿmamb £{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 ˛ Angw
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.
A≤ymbw 22 (Bbp¿±mbZiIƒ) 473
£{X]mssZ LSokap∞m ˛ PkabsØ £{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 ˛ tcsØ ]d™ ]mZ{IaØn¬ XpS¿∂p≈
ZiIfpw ImWWw.
tIjm©ntZhw aXamlp Bcym ˛ CXmWv BNmcy∑mcpsS A`n{]mbw
8. injvSZi ImWp∂ coXn
DZmlcWwPmXIw. tcmlnWn
£{Xw tcmlnWn . £{X KXw 47˛28 1
/ 2
. memw]mZw
£{X]mZw: memw]mZw
Zimcmin aow. ZimmY≥ 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
PinjvSZi 8 h¿jw 4 amkw 6 Znhkw Qjm[n] KpcpZim.
£{Xw 60 mgnI F∂ IW°v CS°meØpsh®p amdnbXnm¬ Ct∏mƒ Hmtcm
ZnhktØbpw £{XmgnI {]tXyIw tmt°≠Xp≠v.]mcºcycoXnbnse
kabm[njvTnXamb KWnXØnte Cu _p≤nap´p≈p. ÿem[njvTnXamb B[pnI
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 ZimmYpw = aow. Kpcp. 10 h¿jw
£{X]mZØn¬ _m°n
53˛20 ˛˛ 50˛33 = 2˛47
3˛20 =10
2˛47 ?
^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
aow taSw CShw anYpw 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{]`rXon `mmw
hmIymn bmy£c]w‡nPmn
tXjmw {ItassWh Zim {]Iev]ym
hmIy{Iaw km[znXn tINnZmlpx
Z{kmZn]mZ{]`rXon `mmw ˛ AizXn XpSßnb £{XßfpsS ]mZ߃°p
hmIymn bmn A£c]w‡nPmn ˛ 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¿Iyfnaok‘u
afiqIKXyizhcπpXn›
knwlmhtemIkv{Xnhn[m XZmow
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, aow ChIfpsS
k‘nIfn¬.(km[mcW Aptema ˛{]Xn
temaKXnIƒ°p ]pdsa Zimcmin Iƒ°v)
afiqIKXn AizhcπpXn N knwlmhtemIx {Xnhn[m -
A≤ymbw 22 (Bbp¿±mbZiIƒ) 475
˛ afiqIKXn, XpcKKXn, knwlmhtemIw
F∂o aq∂p Xcw {]tXyI KXnIƒIqSn D≠v.
XZmow Zim¥cw ZpJ^e{]Zw kymXv ˛ AØcw ZiIƒ tZmj^ew sNøpw.
(1) knwlmhtemIKXn
AizXn {Kq∏n¬, taSwapX¬ aowhscbp≈ ]{¥≠p cminIfpsS Hcp ]cnhrØn
]q¿Ønbm°n, ASpØ ]{¥≠p cminIfpsS ]cnhrØn Bcw`n°p∂Xv hr›nI
ØnemWt√m. aoØn¬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 aow˛hr›nIw, 3 [p˛taSw
`cWn 2 [p˛taSw, 3 aow˛hr›nIw
tcmlnWn 2 hr›nIw˛aow. 3 taSw ˛[p
aIbncw 2 taSw˛[p, 3 hr›nIw˛aow
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
^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∂ coXn
Zimh¿jsØ A]lmcmYs‚ 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
tajmZoIw aZw KtP
Xpμx ]pss›hapZocnXw XXv.
11. £{X]mZ ]cambp v
hmtIyjp.... ˛ (Xmsg) hmIyßfn¬ {]amWambn ]d™n´p≈ h¿jßfmWv Hmtcm
£{X ]mZØns‚bpw ]cambp v.
tajmXv ˛ taSw XpSßnb cminIƒ°v
AoIw aZw KtP Xpμx
001 58 38 68
= 100 85 83 86
Cu {Iaw AizXn, `cWn {Kq∏pIfptSXmWv.
]px 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
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¬ tcsØ ]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{]hNØnv hnwtimØcnZibv°p ]d™
^e߃ tN¿Øp Nn¥n°mhp∂XmWv.
IqSpX¬ -- hnhc߃°pw hnkvXcn® ^e`mKØnpw PmXI]mcnPmXw, {io
apØpkzmanbpsS ImeN{IZi XpSßnb {KŸßƒ klmbn°pw.
(ImeN{IZibnse ZimmY]´nI An_‘w 4˛¬ sImSpØn´p≠v.)
2. DXv]∂ B[m almZiIƒ
(£{XZiIƒ)
(16)
P∑¿£mXv ]cXkvXp ]©a`hm f tYmXv]∂ kw⁄m Zim
kymZm[mZim f ]ytXm f jvSa`hmXv t£am∑lmJym Zim
Bkmtah Zimhkmkatb arXyp{]Zm kym∂rWmw
kz¬]m¬]kambpjmw(1)
{Xnh[]©¿t£ Zimbm¥nta.
(1) ]mTt`Zw ˛ km¬]w Zo¿Lkambpjmw
^eZo]nI 478
1. 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[mZim AjvSa`hmXv ˛ F´mw £{XØns‚ Zi B[mZi.
3. t£amXv almJym Zim. ˛ t£aw ˛ kpJw ˛ mev.
memw £{XØns‚ Zi almZi.
4. Zimhkmkatb arXyp{]Zx kymXv rWmw
˛ Cu ZiIfpsS Ahkm kabw (Zimk‘n
Iƒ) apjy¿°p amcIamWv.
5. kz¬] A¬] ka Bbpjmw ˛ A¬∏mbp v, Zo¿Lmbp v, a≤ymbp v
F∂nßsbp≈ 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{IPohZnIrss±hmIcoWmw kamx
sskz sskzx (1)
]pjvS^em nk¿KPnssXx ]w‡n¿Zimbmx {Iam˛
Zt¥ e·Zim ipt`Xn bhm 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 ZnIrXv ZnhmIcoWmw
N Ip _p ip Kp c a ˛ XpSßnbhcpsS
kamx ˛ (Zim) h¿j߃ BIp∂p.
A≤ymbw 22 (Bbp¿±mbZiIƒ) 479
tkz tkz ]pjvS^emn.... ˛ ZimmY∑m¿°p _eaps≠¶n¬ Ah
chcpsS Zibn¬ ip`^e߃ D≠mIpw.
At¥y e·Zim ipt`Xn bhm ˛ e·ZibpsS Ahkm`mKw ip`sa∂mWv
bhmNmcycpsS A`n{]mbw.
 C—¥n tINnXv XYm ˛ Nne¿ CXntmSp 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 sNømp≠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∂Xnp ]Icw inbpsS AºXp h¿jØn¬ e·Øns‚ ZiIqSn
Dƒs∏Sp∂psh∂ ImcyamWv bhmNmcycpsS 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. AwiIZi
Bbp¿±mbKWnXØnse Hcp {][mZibmWv AwiZi. hcmlanlnc≥ hfsc
_lpamn®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.
^eZo]nI 480
(18)
en]vXoIrXy `tPXv {Klw JLsskvX—njvSambpjvIem
BimJmiznlrXm_vZamkZnhkmx ktXymZntXw f imbpjn
h{InWyp®KtX {XnkwKpWanZw kzmwi{Xn`mtKmØta
ZznLvw oNKtX f ¿[a]yY Zfw autVy knXm¿°o hnm.
1. AwiIZi ImWp∂ hn[w
1. en]vXoIrXy `tPXv {Klw JLsskvX—njvSambpjvIem.....
ktXymZntX Awimbpjn ˛ kXymNmcy≥ ]d™ AwiIZibn¬
{Klw ˛ {Klkv^pSsØ.
en]vXoIrXy ˛ IeIfm°n.
`tPXv JLss.
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∂ hmIyapkcn®v AwiIZibn¬
Hmtcm {Klhpw ¬Ip∂ Bb v B {Klw `pPn® (]n∂n´) hmwiIØnp XpeyamWv.
Hcp hmwiØnv 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∂dnbmmWv 200 sIm≠p lcn°p∂Xv.
Hcp hmwiafiesØ AYhm AwiIN{IsØbmWv 12 kqNn∏n°p∂Xv.
H∂ne[nIap≈ afießsf IeIfnep≈ {Klkv^pSØn¬n∂pw o°mmWv 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.
A≤ymbw 22 (Bbp¿±mbZiIƒ) 481
{Klkv^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 hmwiØnv Hcp h¿jw F∂ IW°n¬ h¿j˛amk˛Znhkßfm°Ww.
2 AwiIZi : KWnXw
DZmlcWPmXIØnse 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 hmwiØnv 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 IqSpXembXnm¬ 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 ZznLvw ....
h{InWyp®KtX...... ˛ h{IØntem D®Øntem D≈ {KlßfpsS
Bbp¿h¿jsØ.
{XnkwKpWanZw ˛ aq∂psIm≠p s]cp°Ww. (aq∂nc´nbm°Ww)
^eZo]nI 482
kzmwi{Xn`mtKmØssax ZznLvw ˛ 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,
kzhmwiw, h¿t§mØahmwiw $ 2 (+)
4. oNauVylcWw
3. oNKtX f ¿[a]yY Zfw autVy knXm¿°o hnm.oNKtXx A¿≤....
oNKtX f ¿[ ˛ oNØnep≈ {KlØns‚ ]IpXn
Ipdbv°Ww.
Zfw autVy knX A¿°o hnm. ˛ ip{I≥, in 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`
{Xywtimw cn]pt` hnm £nXnkpXw ktXym]tZti Zim˛
e·kymwikam _enypZbt` 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
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£{XlcWw
4. {Xywtimw cn]pt` hnm £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,
kzhmwiw, h¿t§mØahmwiw
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∂ hmwiØnp XpeyamWv
e·mbp v,
^eZo]nI 484
6. _enn DZbt`... ˛ e·ØnmWv 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·cmiywiIØnmsW¶n¬ AwiIØnp
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·ØnmsW¶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·kv^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 _lpLvXmbm˛
taI¥p bZv`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 of
multiplications) sIm≠v CXns AtbmKy
am°p∂p.
BNmcyIw Xp A{X ˛ ktXym]tZiw Apkcn®v .
_lpLvXmbmw GI¥p bZv`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®XnptijamWv 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
A≤ymbw 22 (Bbp¿±mbZiIƒ) 485
Ifbp∂Xnm¬ icnbmb coXn hy‡am°pIbmWv ChnsS.
Bbp¿±mbKWnXØn¬ kXymNmcys‚ Cu AwiIZiXs∂bmWv
t{ijvTambn´p≈Xv. ]t£, Amhiyambv 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 KpWw
am{Xw aXn F∂¿∞w.) Ipdbv°ens‚ ImcyØnepw Cu coXnX∂bmWv th≠Xv.
DZmlcWØnv, 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]nn `w hntmZbessh¿n¿≤m XmMvssKx lrXw (1)
XymPyw kuaynco£ntX¿f≤arWa{Xmbpjy`n⁄m hnZpx.
(1) ]mTt`Zw ˛ hntmZbessh¿hnLvw XmwtK lrXw.
1. ]nfiZimh¿j߃
t[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∂, Ap{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 aow 15 6
Kpcp I¿°Sw 5 15 aIcw 5 7 1
/2
ip{I≥ aow 27 21 I ∂n 27 10 1
/2
aμ≥ Xpemw 20 20 taSw 20 10
^eZo]nI 486
2. lcW߃
]q¿hhXv N lcWw k¿hw hnZ[ymZnl ˛ tcsØ AwiImbp¿±mb Ønp ]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¿±mbØnp ]d™Xpt]mse
Øs∂ sNøWw. A©matØXmb {IqtcmZblcWw Cn ]dbp∂p.
3. {IqtcmZblcWw
et· ]m]nn `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.
kuaynco£ntXm... ˛ e·Ønp 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·Zi
e·Zim ss]fimtJy ˛ ]nfimbp¿±mbØnse e·Zi
_ehXn Awti Awikamw ˛ e·Øns‚ AwiIw (e·hmwiw)
_etØmSp IqSnbXmsW¶n¬ AwiI
Ønp kamamb h¿jw.
_ebp‡w bZn e·w cminkaw ˛ e·w _etØmSpIqSnbXmsW¶n¬ cmin°p
Xpeyamb h¿jw.
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∂p
lcWw otN A¿≤w...
1. {Kl߃ D®ØnemsW¶nemWv ta¬∏d™ h¿j߃ In´pI.
2. {Kl߃ oNØnemsW¶n¬ CXn¬ ]IpXn Ipdbpw.
3. D®Ønpw oNØnpw CSbnepw oNØnpw D®Ønpw CSbnepap≈
ÿnXn°v Bbp¿h¿jw ImWm≥ ss{XcminIw sNøWw .
(24)
ss]fiymJyambp¿{_phtX {][mw
aWn∞NmWIyabmZb›
GX∂ km[znXyhZZv`Zt¥m (1)
hcmlkqcyky XtZh hmIyw.
(1) ]mTt`Zw: almt¥m ˛ alm∑m¿
6. A`n{]mbw
ss]fiymJyw Bbpx {_phtX {][mw˛]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≤kymkn / kXymNmcy≥).
^eZo]nI 488
6. Pohi¿ΩZi
(25)
kqcymZnImmw kzatX Poh˛
i¿Ωm kzcmwiw ]cambptjm f {X
Akym]n k¿hw lcWw hnt[bw
]q¿thm‡h√·Zima]ol.
1. kzatX Pohi¿Ωm ˛ Pohi¿Ω F∂ BNmcys‚ A`n{]mbØn¬
kqcymZnImmw ˛ 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 tcsØ ]d™ ˛˛ ]nfiZi
bv°p ]d™ ˛˛ F√m lcW߃°pw
hnt[bamWv.
3. ]q¿thm‡h√·Zima]ol ˛ e·Zibpw tctØ ]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 hnmgnI $ 7 = 120-˛5
]nfiZibv°p ]d™ F√m lcWßfpw CXnpw thWw. e·Zibpw AXp t]mseØs∂.
7. ]pcpjmbp v F{X?
(26)
rWmw ZzmZih’cm ZilXm Bbpx {]amWw ]ssc˛
cmJymXw ]caw isskv{Xn`KtWm bmh÷sscocnXw
tINn®{μkl{kZ¿ianl 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¬ apjycpsS Bbp v q‰ncp]Xv
h¿jamWv
2. ]ssc BJymXw ]caw issx {Xn`KtWm bmhXv Pssx CucnXw ˛
˛ F∂m¬ a‰p NnecpsS A`n{]mbØn¬ inbpsS aq∂p `KWImew
( 30 $ 3) BWv ]cambp v.
A≤ymbw 22 (Bbp¿±mbZiIƒ) 489
3. tINnXv N{μkl{kZ¿ianlt{]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¬ apjymbp v qdp h¿jw
BsW∂mWv. Ωfpw AXntmSp tbmPn°p∂p.
8. Zim{Iaw
(27)
e·mZntXyμpImma[nI_ehXx
kym±imZu XtXm f ym
XXvtI{μmZnÿnXmmanl _lpjp ]p¿˛
hocytXm hocykmtay
_lzmbp¿h¿jZmXpx {]Yaanhim˛
t®mZnXkym_vZkmtay
hocyw InwXz{X k‘n¿{KlhnhclXw
`mhk‘y¥cm]vXw.
1. e· BZnXy Cμp`mmw A[nI_ehXx kymXv ZimZu
˛ e·w, BZnXy≥, N{μ≥Chcn¬ A[nIw _eap≈ {KlØns‚ ZibmWv
BZyw hcpI.
2, XXx Aym XXv tI{μmZn ÿnXmmw Cl
˛ c≠maXmbn tI{μØn¬ n¬°p∂ {KlØns‚ Zi hcpw
3. _lpjp ]px 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 Chti 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....
˛ Cn AYhm hocyw, Zimh¿jw, kqcytbmK Ønptijw BZyw DZn°pI
F∂nhsb√mØnepw HØphcnIbmsW¶n¬ ASpØ ÿmØp≈ {KlsØ
s°m≠p Nn¥n°Ww.
^eZo]nI 490
9. Cu ZiIƒ Nn¥nt°≠sXt∏mƒ
(28)
Awtim¤hw e·_emXv{]km[y˛
ambp› ]ntfim¤ha¿°hocymXv
ssk¿§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 _temmx.
1. e·ØnmWv _ew IqSpXse¶n¬ Awimbp pw
2. kqcymWp _esa¶n¬ ]nfimbp pw
3. N{μmWp _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≠ÆØnp Xpey_ew hcnIbmsW¶n¬ c≠pw XΩn¬ Iq´n
c≠psIm≠p lcn°pI.
6 aq∂npw _eans√¶n¬, Pohi¿ΩobcoXn Apkcn®p Zi ImWpI.
(30)
ImeN{IZim t⁄bm N{μmwtiti _emzntX
kZm £{Xam¿t§W Zim _ehXo kvarXm.
1. N{μmwtiti _emzntX ImeN{IZim t⁄bm
˛ N{μs‚ hmwiØns‚ mYv _eaps≠¶n¬ ImeN{IZi Apkcn®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¿ZznLvm apPIcnWmw ]© N nim
lbmmw Zzm{XnwiXv JcIc`tbmx ]©IIrXnx
hncq]m km Xzmbp¿hrjalnjtbm¿ZzmZi iqmw
kvarXw OmKmZomw ZiIklnXmx jSv N ]caw.
A≤ymbw 22 (Bbp¿±mbZiIƒ) 491
10. ]cambp v
1. jjvTn¿ZznLvm apPIcnWmw... ˛ apjy¿°pw BIƒ°pw q‰n bncp]Xp h¿jw
5 Znhkw
2. lbmmw Zzm{XnwiXv ˛ IpXncbv°v ap∏Ønc≠p h¿jw
3. JcIc`tbmx ]©IIrXnx ˛ H´IØnpw IgpXbv°pw Ccp]Ønb©p
h¿jw
4. hncq]m km]ymbpx hrjalnjtbm˛ Imfbv°pwt]mØnpwCcp]Ønmep h¿jw
5. ZzmZi iqmw ˛ mbbv°p ]{¥≠p h¿jw
6. OmKmZomw ZiIklnXmx jSv ˛ BSnp ]Xnmdp h¿jw
Cu t«mIw tlmcmimkv{XØn¬ --n∂pap≈XmWv. (7˛5)
]cambpx h¿jw
h¿jw
apjy≥, B 120
IpXnc 32
H´Iw, IgpX 25
Imf, t]mØv 24
mb 12
BSv 16
(32)
tb [¿ΩI¿ΩncXm hnPntX{μnbm›
tb]∞yt`mPcXm ZznPtZh`‡mx
tb amhm Z[Xn tb Ipeioekoamw
tXjmanZw IYnXambpcpZmc[o`nx.
11. ]cambp v B¿°p In´pw ?
1. tb [¿ΩI¿ΩncXm ˛ [¿ΩI¿Ωßfn¬ ncXcmbn,
2. hnPntX{μnbm› - ˛ hnPntX{μnbcpambn
3. tb ]∞yt`mPcXm ˛ ]∞y t`mPØn¬ cXcmbn
4. ZznPtZh`‡mx tb amhm Z[Xn˛ {_m“WtZh`‡cmbn
5. tb Ipeioekoamw ˛ Ipeioe߃ Apkcn®v Ignbp∂thm
tXjmanZw ˛ B apjy¿°mWv Cu Bbp v ]dbp∂Xv.
CXpw tlmcbnep≈ t«mIamWv. PmXI]mcnPmXhpw CXv D≤cn°p∂p≠v. .
^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¿ÆbØnp am{Xa√
s]mXphmb ^e{]hNØnpw D]tbmKn°m≥ th≠ am¿§n¿t±ißfpw AhnsS
¬Ip∂p≠v. F∂m¬ GItZiw mqdp 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¿ÆbØnpw
km[mcWKXnbn¬ C∂v ChsbØs∂ B{ibn°p∂p.

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PHALADEEPIKA - CHAPTER 22

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1234567890123456789012345678901212345678901234567890123456789012123456789012345678901234567890121234567890123456789012345678901 Language : Malayalam PHALADEEPIKA (INDIAN ASTROLOGY) CHAPTER TWENTY TWO DIFFERENT SYSTEMS FOR DETERMINING LONGEVITY AUTHOR MANTRESWARA Translation, DTP and Layout by Mullappilly Protected with Copy Right Rules by the TranslatorotecteL
  • 3. A≤ymbw 22 (Bbp¿±mbZiIƒ) 465 A≤ymbw 22 Bbp¿±mbZiIƒ 1. ImeN{IZi 1. ImeN{IZi 2. ImeN{IZi ImWp∂ hn[w 3. £{X]mZßfn¬ cminIfpsS hnymkw 4. khyA]khy£{X߃ 5. ImeN{IZibn¬ {KlßfpsS Zimh¿jw 6. Zim{Iaw (1) AizXn˛Im¿ØnI KW߃ (2) `cWn KWw (3) tcmlnWn KWw (4) aIbncw˛XncphmXnc KW߃ 7 ImeN{IZibv°v ASnÿmamb mep £{XKW߃ 8. injvSZi ImWp∂ hn[w 9 Zim{IaØnse Nne {]tXyIKXnIƒ (1) knwlmhtemIKXn (2, 3) Aizhc˛afiqI KXnIƒ 10. A]lmc߃ ImWp∂ coXn 11. £{X]mZ ]cambp v 12. Zim^ew 2. DXv]∂ B[m almZiIƒ 3. nk¿§Zi 4. AwiIZi 1. AwiIZi ImWp∂ hn[w 2. AwiIZi -˛ KWnXw 3. h{IØnepw D®Ønepw a‰pw n¬ --°p∂ {KlßfpsS Zimh¿j Øn¬ hcp∂ h¿≤ 4. oNauVylcWw 5. Zriym¿≤lcWw 6. i{Xpt£{XlcWw 7. e·mbp v 5. ]nfiZi ( D®oNZi) 1. ]nfiZimh¿j߃ 2. lcW߃ 3. {IqtcmZblcWw 4. e·Zi 5. oNlcWw hy‡am°p∂p 6. A`n{]mbw 6. Pohi¿ΩZi 7. ]pcpjmbp v F{X? 8. Zim{Iaw 9. Cu ZiIƒ Nn¥nt°≠sXt∏mƒ 10. ]cambp v 11. ]cambp v B¿°p In´pw ?
  • 4. ^eZo]nI 466 1. ImeN{IZi tlmcmimkv{XØnse Ggma≤ymbw Bbp¿±mbsØ°pdn®p≈XmWv. D®oNZi, Pohi¿ΩobZi, AwiIZi F∂o aq∂v Bbp¿±mbZiIƒ AhnsS hnhcn°p∂p≠v. ^eZo]nI Ccp]Ønc≠mw A≤ymbØnepw Cu hnjbamWv ssIImcyw sNøp∂Xv. ImeN{IZi (t«mIw 1˛15), D¬∏∂mZmalmZiIƒ (t«mIw 16), nk¿§Zi (17), AwiIZi (t«mIw 18˛20), D®oNZi (t«mIw 21˛24), Pohi¿ΩobZi (t«mIw 25) F∂nßs Bdp ZiIfmWv ChnsS Cu kμ¿`Øn¬ hnhcn°p∂Xv. Chbn¬ ImeN{IZibmWv {]XyI]cnKWtbmsS BZyw hnhcn°p∂Xv. tIcfØnse PmXIßfn¬ ASpØ Imewhsc hnwtimØcn°papºv ImeN{IZi FgpXp∂ ]Xnhp≠mbncp∂p. 1. ImeN{IZi hnwtimØcnZibnset∏mse ImeN{IZibnepw ZiIƒ IW°m°p∂Xv £{Xßsf ASnÿmam°nbmWv. F∂m¬ hnwtimØcnbn¬ N{μ≥ n¬°p∂ £{XamWv BZyZibpw injvSZibpw n›bn°p∂sX¶n¬ ImeN{IZibn¬ Chbv°Snÿmw N{μ≥ n¬°p∂ £{X]mZamWv. cmiym[n]cmWv ImeN{IZibnse ZimmY∑m¿. taSØnp IpP≥, CShØnp ip{I≥, anYpØnp _p[≥ F∂ {IaØn¬ --Xs∂bmWv CXp hcp∂Xv. ^eZo]nI sIm√w]Xn∏n¬ ImeN{IZisb°pdn®p ]Øp t«mIßtf ImWp∂p≈q. DØtc¥y≥ ]Xn∏pIfn¬ ]Xn©p t«mIßfp≠v; sImSpß√p¿ ]Xn∏n¬ ]Xntgp t«mIßfpw. .Cu hnjbØn¬ PmXI]mcnPmXØn¬ ^e`mKhpw hniZmwißfpw AS°w 112 t«mIßfp≠v. Cu A≤ymbØnse hnjbw Bbp¿KWnXambXnm¬ AXnv Bhiyamb KWnX`mKw am{Xta ^eZo]nIbpsS I¿Ømhv ChnsS hnhcn°p∂p≈q. 2 ImeN{IZi ImWp∂ hn[w: : 1. BZyambn PkabsØ £{X]mZw ImWpI. 2. £{X]mZwsh®v PkabsØ cminZi ImWpI. cminmY≥Xs∂bmWv ZimmY≥. 144 ZiIfn¬ GXp ZibnemWv Pw hcp∂sX∂p ImWm≥ 3 apX¬ -- 7 hsc t«mIßfn¬ -- Bhiyamb hnhc߃ Xcp∂p≠v. CXpsh®vv GXp cminZibn¬ BWv Psa∂pw Zimh¿jw F{XbmsW∂pw Ffp∏Øn¬ Is≠Ømw.
  • 5. A≤ymbw 22 (Bbp¿±mbZiIƒ) 467 (1) Z{kmZnXx ]mZhti tajm˛ ∑omwiIm¥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 hnymkw ( tajmXv aomwiIm¥hpw IoSm≤bm¥hpw ) 1. A]khyw ˛ A]khyamb Z{kmZnXx ˛ AizXn apXemb £{XßfpsS (AizXn, `mcWn, Im¿ØnI KWßfpsS) ]mZhti ˛ ]mZ߃°pkrXambn. tajmXv aomwiIm¥w {Iaix˛ taSw apX¬ aowhscbp≈ 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 CXnp hn]coXamWv.) Hcp £{XØnv mep ]mZ߃. Hcp ]mZØnv HºXp ZiIƒ. CXp {]Imcw Hcp £{XØnv 36 ZiIƒ hcpw. 36 ZiIƒ h´saØm≥ ]{¥≠p cminIƒ aq∂p h´w Bh¿Øn®p hcWw. CXn¬ BZysØ ]{¥s≠Æw taSw apX¬ aow hsc F∂p km[mcW{IaØnepw ]ns∂ ]{¥s≠Æw hr›nIw apX¬ -- [phsc F∂p hn]coX {IaØnepw ASpØ ]{¥s≠Æw taSw apX¬ aow hsc F∂ km[mcW {IaØnepw Bh¿Øn®phcpw. (CXp hy‡ambn a nemIm≥ t«mI߃ 5˛9 IqSn ImWWw).
  • 6. ^eZo]nI 468 4. A]khy khy£{X߃ ( Z{kmZnX.....APXmcmXv ) A]khyw (heXv) khyw (CSXv) (2) Ghw `qbm®m]khyw N khyw `mn {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 `mn {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∂) cminmY∑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° cminZimhnymkw hcp∂p≈p. (C°mcyw t«mIw Ggn¬ hy‡am°p∂p≠v.) AXpsIm≠v, Hcp £{XØnv 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 Cn ]dbp∂Xv. (3) apx ]cx kn¿[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.Angw 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
  • 7. A≤ymbw 22 (Bbp¿±mbZiIƒ) 469 5. ImeN{IZibn¬ {KlßfpsS Zimh¿j߃ cmin Nnßw I¿°Sw taSw& anYpw& [p& CShw& aIcw& hr›nIw I∂n aow Xpemw Ipw`w cmiym[n] c N Ip _p Kp ip a ap ]c kn [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 Ap_‘ambn sISpØn´p≠v.) (4) Zim]lmcmZnIImeNt{I hmIymn Z{kmZn]ZmZnPmn h£yman h¿ssÆ¿∂h`n¿`amss˛ cmioih¿ssjx ]cambpc{X. Z{kmZn ]ZmZnPmn ˛ AizXn apXemb £{XßfpsS ]mZßfpsS. Zim]lmcmZnI cminNt{I ˛ ImeN{IZibnse ZiIfpw A]lmcßfpw. hmIymn ˛ 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∂npw mep ]mZ߃. Hcp ]mZØns‚ Iogn¬ 9 cminIƒ. AXmbXv Hcp £{XKWØnv BsI 36 cminIƒ thWw. CXp icnbm°m≥ taSwapX¬°v aowhscbp≈ ]{¥≠p cminIƒ aq∂ph´w Bh¿Øn®p hcWw. Cu Bh¿Øw c≠p hn[ØnemWv. BZyw taSwapX¬ aow 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
  • 8. ^eZo]nI 470 (6) ZmkXthtim Kuco]p{Xw £∂n[nImtcm tKm`qtijw kuZ[n£t{Xlmkt¥m `uaKpcpx ]p{Xmt£mm[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) hmIymtyXmyiznbmay¿£tbm¿tbm˛ yiznymZymy·n`kym]kthy kthyftPtμzm¿h£yamtWjp hmtIy˛ jzntμm¿hmIymtyh cu{Zky `qbx. 1. hmIymn GXmn ˛ Cu hmIy߃. Aiznbman E£tbm ˛ AizXn, `cWn £{XßfpsS
  • 9. A≤ymbw 22 (Bbp¿±mbZiIƒ) 471 (AizXn˛`cWn {Kq∏pIfpsS) mep ]mZß fpsS cminIƒ (Zim{Iaw) BIp∂p. 2 AiznymZymn 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 ˛ Cn ]dbm≥ t]mIp∂ hmIyßfn¬ Ctμm hmIymn Gh ˛ aIbncØns‚ hmIy߃Xs∂ cu{Zky `pb ˛ XncphmXncbv°pw hcp∂p. tcmlnWn, aIbncw {Kq∏pIfpsS ]mZßfpsS cminIƒ Xmsg ]dbp∂p.. CXn¬ aIbncw{Kq∏npw XncphmXnc{Kq∏npw Htc hmIy߃Xs∂bmIp∂p. (8) t[px t£t{X ]pctKm ip`p˛ kvXmkmw P{Xp £∂n[n Zmko N¿amt`mKo cmb[nm£˛ 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
  • 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 ASnÿmamb £{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 ˛ Angw 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.
  • 11. A≤ymbw 22 (Bbp¿±mbZiIƒ) 473 £{X]mssZ LSokap∞m ˛ PkabsØ £{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 ˛ tcsØ ]d™ ]mZ{IaØn¬ XpS¿∂p≈ ZiIfpw ImWWw. tIjm©ntZhw aXamlp Bcym ˛ CXmWv BNmcy∑mcpsS A`n{]mbw 8. injvSZi ImWp∂ coXn DZmlcWwPmXIw. tcmlnWn £{Xw tcmlnWn . £{X KXw 47˛28 1 / 2 . memw]mZw £{X]mZw: memw]mZw Zimcmin aow. ZimmY≥ 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 PinjvSZi 8 h¿jw 4 amkw 6 Znhkw Qjm[n] KpcpZim. £{Xw 60 mgnI F∂ IW°v CS°meØpsh®p amdnbXnm¬ Ct∏mƒ Hmtcm ZnhktØbpw £{XmgnI {]tXyIw tmt°≠Xp≠v.]mcºcycoXnbnse kabm[njvTnXamb KWnXØnte Cu _p≤nap´p≈p. ÿem[njvTnXamb B[pnI 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 ZimmYpw = aow. Kpcp. 10 h¿jw £{X]mZØn¬ _m°n 53˛20 ˛˛ 50˛33 = 2˛47 3˛20 =10 2˛47 ?
  • 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 aow taSw CShw anYpw 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{]`rXon `mmw hmIymn bmy£c]w‡nPmn tXjmw {ItassWh Zim {]Iev]ym hmIy{Iaw km[znXn tINnZmlpx Z{kmZn]mZ{]`rXon `mmw ˛ AizXn XpSßnb £{XßfpsS ]mZ߃°p hmIymn bmn A£c]w‡nPmn ˛ 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¿Iyfnaok‘u afiqIKXyizhcπpXn› knwlmhtemIkv{Xnhn[m XZmow 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, aow ChIfpsS k‘nIfn¬.(km[mcW Aptema ˛{]Xn temaKXnIƒ°p ]pdsa Zimcmin Iƒ°v) afiqIKXn AizhcπpXn N knwlmhtemIx {Xnhn[m -
  • 13. A≤ymbw 22 (Bbp¿±mbZiIƒ) 475 ˛ afiqIKXn, XpcKKXn, knwlmhtemIw F∂o aq∂p Xcw {]tXyI KXnIƒIqSn D≠v. XZmow Zim¥cw ZpJ^e{]Zw kymXv ˛ AØcw ZiIƒ tZmj^ew sNøpw. (1) knwlmhtemIKXn AizXn {Kq∏n¬, taSwapX¬ aowhscbp≈ ]{¥≠p cminIfpsS Hcp ]cnhrØn ]q¿Ønbm°n, ASpØ ]{¥≠p cminIfpsS ]cnhrØn Bcw`n°p∂Xv hr›nI ØnemWt√m. aoØn¬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 aow˛hr›nIw, 3 [p˛taSw `cWn 2 [p˛taSw, 3 aow˛hr›nIw tcmlnWn 2 hr›nIw˛aow. 3 taSw ˛[p aIbncw 2 taSw˛[p, 3 hr›nIw˛aow 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
  • 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∂ coXn Zimh¿jsØ A]lmcmYs‚ 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 tajmZoIw aZw KtP Xpμx ]pss›hapZocnXw XXv. 11. £{X]mZ ]cambp v hmtIyjp.... ˛ (Xmsg) hmIyßfn¬ {]amWambn ]d™n´p≈ h¿jßfmWv Hmtcm £{X ]mZØns‚bpw ]cambp v. tajmXv ˛ taSw XpSßnb cminIƒ°v AoIw aZw KtP Xpμx 001 58 38 68 = 100 85 83 86 Cu {Iaw AizXn, `cWn {Kq∏pIfptSXmWv. ]px 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
  • 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¬ tcsØ ]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{]hNØnv hnwtimØcnZibv°p ]d™ ^e߃ tN¿Øp Nn¥n°mhp∂XmWv. IqSpX¬ -- hnhc߃°pw hnkvXcn® ^e`mKØnpw PmXI]mcnPmXw, {io apØpkzmanbpsS ImeN{IZi XpSßnb {KŸßƒ klmbn°pw. (ImeN{IZibnse ZimmY]´nI An_‘w 4˛¬ sImSpØn´p≠v.) 2. DXv]∂ B[m almZiIƒ (£{XZiIƒ) (16) P∑¿£mXv ]cXkvXp ]©a`hm f tYmXv]∂ kw⁄m Zim kymZm[mZim f ]ytXm f jvSa`hmXv t£am∑lmJym Zim Bkmtah Zimhkmkatb arXyp{]Zm kym∂rWmw kz¬]m¬]kambpjmw(1) {Xnh[]©¿t£ Zimbm¥nta. (1) ]mTt`Zw ˛ km¬]w Zo¿Lkambpjmw
  • 16. ^eZo]nI 478 1. 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[mZim AjvSa`hmXv ˛ F´mw £{XØns‚ Zi B[mZi. 3. t£amXv almJym Zim. ˛ t£aw ˛ kpJw ˛ mev. memw £{XØns‚ Zi almZi. 4. Zimhkmkatb arXyp{]Zx kymXv rWmw ˛ Cu ZiIfpsS Ahkm kabw (Zimk‘n Iƒ) apjy¿°p amcIamWv. 5. kz¬] A¬] ka Bbpjmw ˛ A¬∏mbp v, Zo¿Lmbp v, a≤ymbp v F∂nßsbp≈ 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{IPohZnIrss±hmIcoWmw kamx sskz sskzx (1) ]pjvS^em nk¿KPnssXx ]w‡n¿Zimbmx {Iam˛ Zt¥ e·Zim ipt`Xn bhm 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 ZnIrXv ZnhmIcoWmw N Ip _p ip Kp c a ˛ XpSßnbhcpsS kamx ˛ (Zim) h¿j߃ BIp∂p.
  • 17. A≤ymbw 22 (Bbp¿±mbZiIƒ) 479 tkz tkz ]pjvS^emn.... ˛ ZimmY∑m¿°p _eaps≠¶n¬ Ah chcpsS Zibn¬ ip`^e߃ D≠mIpw. At¥y e·Zim ipt`Xn bhm ˛ e·ZibpsS Ahkm`mKw ip`sa∂mWv bhmNmcycpsS A`n{]mbw. C—¥n tINnXv XYm ˛ Nne¿ CXntmSp 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 sNømp≠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∂Xnp ]Icw inbpsS AºXp h¿jØn¬ e·Øns‚ ZiIqSn Dƒs∏Sp∂psh∂ ImcyamWv bhmNmcycpsS 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. AwiIZi Bbp¿±mbKWnXØnse Hcp {][mZibmWv AwiZi. hcmlanlnc≥ hfsc _lpamn®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.
  • 18. ^eZo]nI 480 (18) en]vXoIrXy `tPXv {Klw JLsskvX—njvSambpjvIem BimJmiznlrXm_vZamkZnhkmx ktXymZntXw f imbpjn h{InWyp®KtX {XnkwKpWanZw kzmwi{Xn`mtKmØta ZznLvw oNKtX f ¿[a]yY Zfw autVy knXm¿°o hnm. 1. AwiIZi ImWp∂ hn[w 1. en]vXoIrXy `tPXv {Klw JLsskvX—njvSambpjvIem..... ktXymZntX Awimbpjn ˛ kXymNmcy≥ ]d™ AwiIZibn¬ {Klw ˛ {Klkv^pSsØ. en]vXoIrXy ˛ IeIfm°n. `tPXv JLss. 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∂ hmIyapkcn®v AwiIZibn¬ Hmtcm {Klhpw ¬Ip∂ Bb v B {Klw `pPn® (]n∂n´) hmwiIØnp XpeyamWv. Hcp hmwiØnv 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∂dnbmmWv 200 sIm≠p lcn°p∂Xv. Hcp hmwiafiesØ AYhm AwiIN{IsØbmWv 12 kqNn∏n°p∂Xv. H∂ne[nIap≈ afießsf IeIfnep≈ {Klkv^pSØn¬n∂pw o°mmWv 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.
  • 19. A≤ymbw 22 (Bbp¿±mbZiIƒ) 481 {Klkv^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 hmwiØnv Hcp h¿jw F∂ IW°n¬ h¿j˛amk˛Znhkßfm°Ww. 2 AwiIZi : KWnXw DZmlcWPmXIØnse 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 hmwiØnv 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 IqSpXembXnm¬ 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 ZznLvw .... h{InWyp®KtX...... ˛ h{IØntem D®Øntem D≈ {KlßfpsS Bbp¿h¿jsØ. {XnkwKpWanZw ˛ aq∂psIm≠p s]cp°Ww. (aq∂nc´nbm°Ww)
  • 20. ^eZo]nI 482 kzmwi{Xn`mtKmØssax ZznLvw ˛ 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, kzhmwiw, h¿t§mØahmwiw $ 2 (+) 4. oNauVylcWw 3. oNKtX f ¿[a]yY Zfw autVy knXm¿°o hnm.oNKtXx A¿≤.... oNKtX f ¿[ ˛ oNØnep≈ {KlØns‚ ]IpXn Ipdbv°Ww. Zfw autVy knX A¿°o hnm. ˛ ip{I≥, in 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` {Xywtimw cn]pt` hnm £nXnkpXw ktXym]tZti Zim˛ e·kymwikam _enypZbt` 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
  • 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£{XlcWw 4. {Xywtimw cn]pt` hnm £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, kzhmwiw, h¿t§mØahmwiw 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∂ hmwiØnp XpeyamWv e·mbp v,
  • 22. ^eZo]nI 484 6. _enn DZbt`... ˛ e·ØnmWv 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·cmiywiIØnmsW¶n¬ AwiIØnp 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·ØnmsW¶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·kv^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 _lpLvXmbm˛ taI¥p bZv`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 of multiplications) sIm≠v CXns AtbmKy am°p∂p. BNmcyIw Xp A{X ˛ ktXym]tZiw Apkcn®v . _lpLvXmbmw GI¥p bZv`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®XnptijamWv 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
  • 23. A≤ymbw 22 (Bbp¿±mbZiIƒ) 485 Ifbp∂Xnm¬ icnbmb coXn hy‡am°pIbmWv ChnsS. Bbp¿±mbKWnXØn¬ kXymNmcys‚ Cu AwiIZiXs∂bmWv t{ijvTambn´p≈Xv. ]t£, Amhiyambv 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 KpWw am{Xw aXn F∂¿∞w.) Ipdbv°ens‚ ImcyØnepw Cu coXnX∂bmWv th≠Xv. DZmlcWØnv, 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]nn `w hntmZbessh¿n¿≤m XmMvssKx lrXw (1) XymPyw kuaynco£ntX¿f≤arWa{Xmbpjy`n⁄m hnZpx. (1) ]mTt`Zw ˛ hntmZbessh¿hnLvw XmwtK lrXw. 1. ]nfiZimh¿j߃ t[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∂, Ap{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 aow 15 6 Kpcp I¿°Sw 5 15 aIcw 5 7 1 /2 ip{I≥ aow 27 21 I ∂n 27 10 1 /2 aμ≥ Xpemw 20 20 taSw 20 10
  • 24. ^eZo]nI 486 2. lcW߃ ]q¿hhXv N lcWw k¿hw hnZ[ymZnl ˛ tcsØ AwiImbp¿±mb Ønp ]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¿±mbØnp ]d™Xpt]mse Øs∂ sNøWw. A©matØXmb {IqtcmZblcWw Cn ]dbp∂p. 3. {IqtcmZblcWw et· ]m]nn `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. kuaynco£ntXm... ˛ e·Ønp 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·Zi e·Zim ss]fimtJy ˛ ]nfimbp¿±mbØnse e·Zi _ehXn Awti Awikamw ˛ e·Øns‚ AwiIw (e·hmwiw) _etØmSp IqSnbXmsW¶n¬ AwiI Ønp kamamb h¿jw. _ebp‡w bZn e·w cminkaw ˛ e·w _etØmSpIqSnbXmsW¶n¬ cmin°p Xpeyamb h¿jw.
  • 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∂p lcWw otN A¿≤w... 1. {Kl߃ D®ØnemsW¶nemWv ta¬∏d™ h¿j߃ In´pI. 2. {Kl߃ oNØnemsW¶n¬ CXn¬ ]IpXn Ipdbpw. 3. D®Ønpw oNØnpw CSbnepw oNØnpw D®Ønpw CSbnepap≈ ÿnXn°v Bbp¿h¿jw ImWm≥ ss{XcminIw sNøWw . (24) ss]fiymJyambp¿{_phtX {][mw aWn∞NmWIyabmZb› GX∂ km[znXyhZZv`Zt¥m (1) hcmlkqcyky XtZh hmIyw. (1) ]mTt`Zw: almt¥m ˛ alm∑m¿ 6. A`n{]mbw ss]fiymJyw Bbpx {_phtX {][mw˛]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≤kymkn / kXymNmcy≥).
  • 26. ^eZo]nI 488 6. Pohi¿ΩZi (25) kqcymZnImmw kzatX Poh˛ i¿Ωm kzcmwiw ]cambptjm f {X Akym]n k¿hw lcWw hnt[bw ]q¿thm‡h√·Zima]ol. 1. kzatX Pohi¿Ωm ˛ Pohi¿Ω F∂ BNmcys‚ A`n{]mbØn¬ kqcymZnImmw ˛ 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 tcsØ ]d™ ˛˛ ]nfiZi bv°p ]d™ ˛˛ F√m lcW߃°pw hnt[bamWv. 3. ]q¿thm‡h√·Zima]ol ˛ e·Zibpw tctØ ]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 hnmgnI $ 7 = 120-˛5 ]nfiZibv°p ]d™ F√m lcWßfpw CXnpw thWw. e·Zibpw AXp t]mseØs∂. 7. ]pcpjmbp v F{X? (26) rWmw ZzmZih’cm ZilXm Bbpx {]amWw ]ssc˛ cmJymXw ]caw isskv{Xn`KtWm bmh÷sscocnXw tINn®{μkl{kZ¿ianl 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¬ apjycpsS Bbp v q‰ncp]Xv h¿jamWv 2. ]ssc BJymXw ]caw issx {Xn`KtWm bmhXv Pssx CucnXw ˛ ˛ F∂m¬ a‰p NnecpsS A`n{]mbØn¬ inbpsS aq∂p `KWImew ( 30 $ 3) BWv ]cambp v.
  • 27. A≤ymbw 22 (Bbp¿±mbZiIƒ) 489 3. tINnXv N{μkl{kZ¿ianlt{]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¬ apjymbp v qdp h¿jw BsW∂mWv. Ωfpw AXntmSp tbmPn°p∂p. 8. Zim{Iaw (27) e·mZntXyμpImma[nI_ehXx kym±imZu XtXm f ym XXvtI{μmZnÿnXmmanl _lpjp ]p¿˛ hocytXm hocykmtay _lzmbp¿h¿jZmXpx {]Yaanhim˛ t®mZnXkym_vZkmtay hocyw InwXz{X k‘n¿{KlhnhclXw `mhk‘y¥cm]vXw. 1. e· BZnXy Cμp`mmw A[nI_ehXx kymXv ZimZu ˛ e·w, BZnXy≥, N{μ≥Chcn¬ A[nIw _eap≈ {KlØns‚ ZibmWv BZyw hcpI. 2, XXx Aym XXv tI{μmZn ÿnXmmw Cl ˛ c≠maXmbn tI{μØn¬ n¬°p∂ {KlØns‚ Zi hcpw 3. _lpjp ]px 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 Chti 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.... ˛ Cn AYhm hocyw, Zimh¿jw, kqcytbmK Ønptijw BZyw DZn°pI F∂nhsb√mØnepw HØphcnIbmsW¶n¬ ASpØ ÿmØp≈ {KlsØ s°m≠p Nn¥n°Ww.
  • 28. ^eZo]nI 490 9. Cu ZiIƒ Nn¥nt°≠sXt∏mƒ (28) Awtim¤hw e·_emXv{]km[y˛ ambp› ]ntfim¤ha¿°hocymXv ssk¿§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 _temmx. 1. e·ØnmWv _ew IqSpXse¶n¬ Awimbp pw 2. kqcymWp _esa¶n¬ ]nfimbp pw 3. N{μmWp _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≠ÆØnp Xpey_ew hcnIbmsW¶n¬ c≠pw XΩn¬ Iq´n c≠psIm≠p lcn°pI. 6 aq∂npw _eans√¶n¬, Pohi¿ΩobcoXn Apkcn®p Zi ImWpI. (30) ImeN{IZim t⁄bm N{μmwtiti _emzntX kZm £{Xam¿t§W Zim _ehXo kvarXm. 1. N{μmwtiti _emzntX ImeN{IZim t⁄bm ˛ N{μs‚ hmwiØns‚ mYv _eaps≠¶n¬ ImeN{IZi Apkcn®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¿ZznLvm apPIcnWmw ]© N nim lbmmw Zzm{XnwiXv JcIc`tbmx ]©IIrXnx hncq]m km Xzmbp¿hrjalnjtbm¿ZzmZi iqmw kvarXw OmKmZomw ZiIklnXmx jSv N ]caw.
  • 29. A≤ymbw 22 (Bbp¿±mbZiIƒ) 491 10. ]cambp v 1. jjvTn¿ZznLvm apPIcnWmw... ˛ apjy¿°pw BIƒ°pw q‰n bncp]Xp h¿jw 5 Znhkw 2. lbmmw Zzm{XnwiXv ˛ IpXncbv°v ap∏Ønc≠p h¿jw 3. JcIc`tbmx ]©IIrXnx ˛ H´IØnpw IgpXbv°pw Ccp]Ønb©p h¿jw 4. hncq]m km]ymbpx hrjalnjtbm˛ Imfbv°pwt]mØnpwCcp]Ønmep h¿jw 5. ZzmZi iqmw ˛ mbbv°p ]{¥≠p h¿jw 6. OmKmZomw ZiIklnXmx jSv ˛ BSnp ]Xnmdp h¿jw Cu t«mIw tlmcmimkv{XØn¬ --n∂pap≈XmWv. (7˛5) ]cambpx h¿jw h¿jw apjy≥, B 120 IpXnc 32 H´Iw, IgpX 25 Imf, t]mØv 24 mb 12 BSv 16 (32) tb [¿ΩI¿ΩncXm hnPntX{μnbm› tb]∞yt`mPcXm ZznPtZh`‡mx tb amhm Z[Xn tb Ipeioekoamw tXjmanZw IYnXambpcpZmc[o`nx. 11. ]cambp v B¿°p In´pw ? 1. tb [¿ΩI¿ΩncXm ˛ [¿ΩI¿Ωßfn¬ ncXcmbn, 2. hnPntX{μnbm› - ˛ hnPntX{μnbcpambn 3. tb ]∞yt`mPcXm ˛ ]∞y t`mPØn¬ cXcmbn 4. ZznPtZh`‡mx tb amhm Z[Xn˛ {_m“WtZh`‡cmbn 5. tb Ipeioekoamw ˛ Ipeioe߃ Apkcn®v Ignbp∂thm tXjmanZw ˛ B apjy¿°mWv Cu Bbp v ]dbp∂Xv. CXpw tlmcbnep≈ t«mIamWv. PmXI]mcnPmXhpw CXv D≤cn°p∂p≠v. .
  • 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¿ÆbØnp am{Xa√ s]mXphmb ^e{]hNØnpw D]tbmKn°m≥ th≠ am¿§n¿t±ißfpw AhnsS ¬Ip∂p≠v. F∂m¬ GItZiw mqdp 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¿ÆbØnpw km[mcWKXnbn¬ C∂v ChsbØs∂ B{ibn°p∂p.