সন্ধি,সন্ধির প্রকারভেদ,ণত্ব বিধান ও ষত্ব বিধান,লিঙ্গান্তরবাচক শব্দ

evsjv

Lecture-03

Av‡jvP¨ welqÑ(evsjv 2q cÎt- mwÜ, mwÜi cÖKvi‡f`, Y-Z¡ I l-Z¡ weavb, wj½evPK kã) (evsjv 1q cÎt-Kwe I mvwnZ¨ welqK Av‡jvPbvt-

we¯ÍvwiZ Av‡jvPbvt-

Av‡jvP¨ welq t mwÜ

mwÜi D‡Ïk¨

(K)mwÜi D‡Ï‡k¨ ¯^vfvweK D”Pi‡Y mnRcÖeYZv Ges (L) aŸwbMZ gvayh© m¤úv`b | †hgb: ÔAvkvÕ I AZxZÕ D”Pvi‡Y †h Avqvm cÖ‡qvRb, ÔAvkvZxZÕ Gi †P‡q mn‡R D”PvwiZ Ges kÖæwZgayi| ZvB †h †ÿ‡Î Avqv‡mi jvNe nq wKš‘ aŸwb-gvayhh© iwÿZ nq bv, †m †ÿ‡Î mwÜ Kivi wbqg †bB| †hgb- KPz + Av`v + Avjy= Kv”Pv`vjy nq bv| A_ev KPz + Avjy + Av`v = Kv”Pvj¦v`v nq bv

Avgiv cÖ_‡g LuvwU evsjv k‡ãi mwÜ I c‡i Zrmg (ms¯‹…Z) k‡ãi mwÜ m¤^‡Ü Av‡jvPbv Kie| D‡jøL¨, Zrmg mwÜ g~jZ eY© ms‡hvM wbqg|

evsjv k‡ãi mwÜ

evsjv mwÜ `y iK‡gi : ¯^imwÜ I e¨ÄbmwÜ

ª ¯^imwÜ : ¯^imwÜ m‡½ ¯^iaŸwb wg‡j †h mwÜ nq Zv‡K ¯^imwÜ e‡j|

1. mwÜ‡Z `y‡Uv mwbœwnZ ¯^‡ii GKwUi †jvc nq | †hgb-

(K) A + G = G (A †jvc) ‡hgb: kZ + GK = k‡ZK| G i~c-K‡ZK

(L) Av + Av = Av (GKwU Av †jvc)| †hgb: kvuLv + Avwi = kvuLvwi| G iƒc- iæcv + Avwj = iƒcvwj

(M) Av + D = D ( Av †jvc)|‡hgb: wg_¨v + DK = wg_y¨K| G iƒc- wnsmyK, wb›`yK BZ¨vw`|

(N) B + G = B (& G †jvc) | †hgb- Kzwo + GK = KzwoK| G iƒc-

awbK, ¸wUK BZ¨vw` | Avwk + Gi = Avwki (G †jvc) G iƒc-( b`xi

+ Gi)

2. †Kv‡bv †Kv‡bv ¯’‡j cvwkvcvwk `y‡Uv ¯^‡ii †k‡liwU †jvc cvq| †hgb- hv + B”Qv + ZvB =hv‡”QZvB| GLv‡b (Av + B) Gi g‡a¨ B †jvc †c‡q‡Q|

ª e¨Äb mwÜ: ¯^‡i Avi e¨Ä‡b Avi e¨Ä‡b Ges e¨Ä‡b Avi ¯^‡i wgwjZ n‡q †h mwÜ nq Zv‡K e¨Äb mwÜ e‡j| cÖK…Z evsjv e¨Äb mwÜ mgxfeb Gi wbq‡gB n‡q _v‡K|Avi Zv-I g~jZ K_¨ ixwZ‡Z mxgve×|

1. cÖ_g aŸwb A‡Nvl Ges cieZx© aŸwb †Nvl n‡j, `y‡Uv wg‡j †Nvl aŸwb wØZ¡ nq| A_©vr mwÜ‡Z †Nvl aŸwbi c~e©eZx A‡Nvl aŸwbI †Nvl nq| †hgb -‡QvU + `v = †QŠo`v|

2. njšÍ i (e× Aÿi wewkó ) aŸwbi c‡i AY¨ eÄb aŸwb _v‡j i jyß n‡q cieZx© aŸwb wØZ¡ nq| †hgb:Avi + bv = Avbœv, Pvi + wU = PvwÆ, `i + bv = abœv, `yi + QvB = `y”QvB BZ¨vw`|

3. P-eMx©q aŸwbi Av‡M hw` Z-eMx©q aŸwb Av‡m Zv n‡j, `-eMx©q aŸwb †jvc nq Ges P-eMx©q aŸwbi wØZ¡ nq| A_©vr Z-eMx©q aŸwb I P-eMx©q aŸwbi cvkvcvwk G‡j cÖagwU jyß n‡q cieZx© aŸwbwU wØZ¡ nq| †hgb: bvZ + RvgvB = bv¾vgvB (Z + R = ¾) e`& + RvZ = e¾vZ, nvZ + Qvwb = nv”Qvwb BZ¨vw`|

4. P-Gi c‡i ÔkÕ Ges Z Gi c‡i ÔmÕ G‡j P I Z Gi ¯’‡j k nq| †hgb- cuvP + k = cuvk&k| mvZ + k = mvk&k, cvuP + wmKv = cuvk&wkKv|

5. njšÍ aŸwbi mv‡_ ¯^iaŸwb hy³ n‡j ¯^‡ii †jvc nq bv| †hgb- †evb + AvB = †evbvB, Pzb + Avwi = Pzbvwi, wZb + GK= wZ‡jK, evi + GK = ev‡iK, wZb + GK = wZ‡bK|

6. ¯^iaŸwbi c‡i e¨ÄbaŸwb Gj ¯^iaŸwbwU jyß nq| †hgb-KuvPv+ Kiv = KuvPKjv, bvwZ + †eŠ = bvZ‡eŠ, †Nvov + †`Šo = †Nvo‡`Šo, †Nvov + Mvwo = †NvovMvwo BZ¨vw`|

Zrmg k‡ãi mwÜ

evsjv fvlvq eû ms¯‹…Z kã Avwe®‹…Z Ae¯’vq i‡q‡Q| G me kãB Zrmg (Zr = Zvi + mg = mgvb) Zvi mgvb A_©vr ms¯‹…‡Zi mgvb| G †kªYxi k‡ãi mwÜ ms¯‹…Z fvlvi wbq‡gB n‡q G‡m‡Q|

evsjv fvlvq e¨eüZ Zrmg mwÜ wZb cÖKvi: (1) ¯^imwÜ (2) e¨Äb mwÜ (3) wemM© mwÜ

v¯^imwÜ: ¯^iaŸwbi m‡½ ¯^iaŸwbi wgj‡bi bvg ¯^imwÜ|

1. A-Kvi wKsev A-Kv‡ii ci A-Kvi wKsev Av-Kvi _vK‡j Df‡q wg‡j Av-Kvi nq, Av-Kvi c~e©eZx e¨Ä‡bi m‡½ hy³ nq| ‡hgbt A + A = Av, bi + Aag = bivag|G iƒc- wngvPj, cÖvYvwaK, n¯ÍvšÍi, wnZvwnZ BZ¨vw`|

A + Av = Av, wng + Avjvq = wngvjq| G iƒc- ‡`evjq , iZœvKi, wmsnvm BZ¨vw`|

Av + A = Av h_v + A_© = h_v_©|G iƒc- AvkvZxZ, K_vg„Z, gnvN© BZ¨vw`

Av + Av = Av , we`¨v + Avjq= we`¨vjq| G iƒc- KvivMvi, gnvkq, m`vb›` BZ¨vw`|

2. A-Kvi wKsev Av-Kv‡ii ci B-Kvi wKsev C-Kvi _vK‡j Df‡q wg‡j G-Kvi nq; G-Kvi c~eeZx© e¨Ä‡bi m‡h&M hy³ nq| †hgb-

A + B = G ïf + B”Qv = ï‡f”Qv

Av + B = G h_v + Bó = h‡_ó

A+ C = G cik + Ck = ci‡gk

Av + C = G gnv + Ck = g‡nk

G iƒc-c~‡Y©›`y, kªe‡Yw›`ªq, †¯^”Qv, b‡ik, i‡gk, b‡i›`ª BZ¨vw`|

3. A-Kvi wKsev Av-Kv‡ii ci D-Kvi wKsev D-Kvi _vK‡j Df‡q wg‡j I-Kvi nq; I-Kvi c~e©eZx© e¨Ä‡b hy³ nq| †ghb:

A + D = I m~h© + D`q = my‡h©v`q|

Av + D = I h_v + DwPZ = h‡_vwPZ

A + D = I M„n + DaŸ© = M„‡nvaŸ©

Av + E = I M½v + Ewg© = M‡½vwg©

&G iƒc- bx‡jvrcj, P‡jvwg©, g‡nvrme, b‡evpv, d‡jv`q, h‡_vchy³, wn‡Zvc‡`k, c‡ivcKvi, cÖ‡kœvËi BZ¨vw`|

4. A-Kvi wKsev Av-Kv‡ii ci F-Kvi _vK‡j Df‡q wg‡j ÔAiÕ nq Gfs Zv †id ( & ) iƒ‡c cieZx© e‡b©j mv‡_ †jLv nq| †hgb-

A + F = Ai ‡`e + Fwl = †`ewl©

Av + F = Ai gnv + Fwl= gnwl©

5. A-Kvi wKsev Av-Kv‡ii ci ÔFZÕ kã _vK‡j A, Av+F Dfq wg‡j ÔAviÕ nq Ges evbv‡b c~eeZx© e‡Y© Av I cieZx© e‡b© †id †jLv nq| †hgb:

A + F = Avi kxZ + FZ = kxZvZ©

Av + F = Avi Z…òv + FZ = Z…òvZ©

6. A-Kvi wKsev Av-Kv‡ii ci G-Kvi wKsev H-Kvi _vK‡j Df‡q wg‡j H-Kvi nq; H-Kvi c~eeZx© e¨Ä‡bi m‡_ hy³ nq| †hgb:

A + G = H Rb + GK = R‰bK

Av + G = H m`v + Ge = m‰`e

A + H = H gZ + HK¨ = g‰ZK¨

Av + H = H gnv + Hk¦h© = g‰nk¦h©

G iyc- wn‰Zlx, m‰e©e, AZz‰jk¦h© BZ¨vw`|

7. A-Kvi wKsev Av-Kv‡ii ci I-Kvi wKsev J-Kvi _vK‡j Df‡q wg‡j J-Kvi nq|J-Kvi c~e©eZx© e¨Ä‡bi mv‡_ hy³ nq| †hgb:

A + I = J eb + Ilwa = e‡bŠlwa

Av + I = J gnv + Jlwa = g‡nŠlwa

A + J = J cig + Jla = ci‡gŠla

Av + J = J gnv + Jla= g‡nŠla

8. B-Kvi wKsev C-Kv‡ii ci B-Kvi wKsev C-Kvi _vK‡j Df‡q wg‡j `xN© C-Kvi nq| `xN© C-Kvi c~eeZx© e¨Ä‡bi mv‡_ hy&³ nq|‡hgb:

B + B = C AwZ + BZ = AZxZ

B + C = C cwi + Cÿv = cixÿv

C + B = C mZx + B›`ª = mZx›`ª

C + C = C mZx + Ck = mZxk

G-iƒc: wMix›`ª, wÿZxk, gnx›`ª, kÖxk, c„_¡xk, AZxe, cÖZxÿv, AZxZ, iex›`ª, w`jøxk¦i BZ¨vw`|

9. B-Kvi wKsev C-Kv‡ii ci B I C wfbœ Ab¨ ¯^i _vK‡j B ev C ÔhÕ nq| h-djv †jLvi mgq c~e©eZx© e¨Ä‡bi mv‡_ wjLv nq| †hgb:

B + A = h& + A AwZ + AšÍ = AšÍ¨šÍ

B + Av = h& + Av BwZ + Avw` = BZ¨vw`

B + D = h& + D AwZ + Dw³ = AZz¨w³

B + E = h& + E cÖwZ + El = cÖZz¨l

C + Av = h& + Av gmx + Avavi = gm¨vavi

B + G = h& + G cÖwZ + GK = cÖ‡Z¨K

C + A = h& + A b`x + A¤^y = b`¨¤^y

G iƒc- cÖZ¨n, AZ¨waK, MZ¨šÍi, cÖZ¨vkv, cÖZ¨veZ©b, Av`¨šÍ, h`¨wc, ch©šÍ, Afz¨Ìvbg AMœyrcvZ, AZ¨vðh© cÖZy¨cKvi BZ¨vw`|

10. D-Kvi wKsev E-Kv‡ii ci D-Kvi _vK‡j Df‡q wg‡j E-Kvi nq; E-Kvi cye©eZx© e¨n&Rb aŸwbi mv‡_ hy³ nq| †hgb:

D + D = E giæ + D`¨vb = giƒ`¨vb

D + E = &E eû + EaŸ© =en~aŸ©

E + D = E ea~ + Drme = eayrme

E + E = E f~ + EaŸ© = f~aŸ©

11. D-Kvi wKsev E-Kv‡ii c‡i D-Kvi I E-Kvi wfbœ Ab¨ ¯^i _vK‡j D ev E e-djv nq Ges †jLvi mgq e-djv c~e©eZx© e‡b©i mv‡_ †jLv nq| †hgb;

D + A = e + A my + Aí = ¯^í

D + Av = e + Av my + AvMZ = ¯^vMZ

D + B = e + B Aby + BZ = Awš^Z

D + C = e + C Zby + C = Zš^x

D + G = e + G Aby + GlY = A‡š^lY

Giƒc: ck¦ag, ck¦vPvi, Aš^q, gš^šÍi BZ¨vw`|

12. F-Kv‡ii ci F wfbœ Ab¨ ¯^i _vK‡j ÔFÕ ¯’v‡b ÔiÕ Ges i-djv c~eeZx© e¨Ä‡bi m‡½ hy³ nq| †hgb-wcZ… + Avjvq = wcÎvjq, wcZ… + Av‡`k = wcÎv‡`k|

13. G , H, I , J-Kv‡i ci G, H ¯’v‡m h_vµ‡g Aq, Avq Ges I, J ¯’v‡b h_vµ‡g Ae I Ave nq| †hgb;

G + A = Aq& + A=†b + Ab = bqb, ‡k + Ab = kqb

H + A = Aq& + A=ˆb + AK = bvqK, ‰M + AK = MvqK

I + A = Ae + A=†cv + Ab = ceb, ‡jv + Ab = jeb

J + A = Ave& + A= †cŠ + AK = cveK,

I + Av = Ae + Av= ‡Mv + Avw` = Mevw`

I + G = Ae& + G= ‡Mv + GlYv = M‡elYv

I + B = Ae& + B = ‡cv + BÎ= cweÎ

J + B = Ave& + B= ‡bŠ + BK = bvweK

J + D = Ave = D= ‡fŠ = DK = fveyK

14. KZK¸‡jv mwÜ †Kv‡bv wbqg Abymv‡i nq bv, G‡`i‡K wbcvZ‡b wm× e‡j| h_v- Kzj + AUv = KzjUv (KzjvUv bq), †Mv + Aÿ = Mevÿ (Meÿ bq), cÖ + Ep = †cÖŠp (‡cÖvp bq), Ab¨ + Ab¨ = Ab¨vb¨, gvZ© + Ab&h = gvZ©Û, ï× + I`b = ï‡×v`b|

ve¨ÄbmwÜt ¯^‡i-e¨Ä‡b, e¨Ä‡b-¯^‡i I e¨Ä‡b-e¨Ä‡b †h mwÜ nq Zv‡K e¨Äb mwÜ e‡j| G w`K †_‡K e¨Äb mwÜ‡K wZb fv‡M fvM Kiv hvq h_v:

(1) e¨ÄbaŸwb + ¯^iaŸwb (2) ¯^iaŸwb = e¨ÄbaŸwb

(3) e¨Äb aŸwb + e¨ÄbaŸwb

1. K, P, U, Z c-Gi c‡i ¯^iaŸwb _vK‡j †m¸‡jv h_vµ‡g M&, R&, (o&) , `&, e& nq| cieZx© ¯^iaŸwbwU cye©eZx© e¨ÄbaŸwbi m‡½ hy³ nq| †hgb:

K +A = M w`K + AšÍ = w`MšÍ

P& + A = R wYP + AšÍ = wYRšÍ

U& + Av = W lU + Avbb = lovbb

c& + A = e myc + AšÍ = myešÍ

GiæcÑ evMxk, Z`šÍ, evMvo¤^i, K…`šÍ, m`vb›`, m`ycvq, m`yc‡`k, RMw`›`ª BZ¨vw`|

2. ¯^iaŸwb + e¨ÄbaŸwb

¯^iaŸwbi ci P _vK‡j D³ e¨ÄbaŸwbwU wØZ¡ (”Q) nq| h_v

A + Q = ”Q GK + QÎ =GK”QÎ

Av + Q = ”Q K_v + Q‡j = K_v”Q‡j

B + Q = ”Q cwi + Q` = cwi”Q`

Giƒc: gyL”Qwe, we‡”Q`, cwi‡”Q`, wew”Qbœ, A½‡”Q`, Av‡jvK”QUv, cÖwZ”Qwe, cÖ”Q`g cÖ”Q`, Av”Qv`b, e„ÿ”Qvqvg ¯^‡”Q‡›` cÖf…wZ|

3. e¨ÄbaŸwb + e¨ÄbaŸwb

(K) 1. Z I `-Gi c‡i P I Q _vK‡j Z I ` ¯’v‡b P nq| †hgb;

Z + P = ”P mr + wPšÍv = mw”PšÍv

Z + Q = ”Q Dr + †Q` = D‡”Q`

` + P = ”P wec` + Pq = wec”Pq

` + Q = ”Q wec` + Qvqv = wec”Qvqv

Giƒc: D”PviY, ki”P›`ª, m”PwiÎg Z”Qwe, mw”P`vb›` cÖf„wZ|

2. Z I ` Gi ci R& F _vK‡j Z I ` Gi ¯’v‡b R nq | †hgb;

Z + R = ¾ mr + Rb = m¾b

` + R = ¾ wec` + Rvj = wec¾vj

Z + S = À K…r + SwUKv = KzÀwUKv

Giƒc: D¾¡j, Z¾b¨, hve¾xeb, RM¾xeb BZ¨vw`|

3.Z I ` Gi ci k _vK‡j Z I ` Gi ¯’‡j P Ges k-Gi ¯’‡j Q D”PvwiZ nq| †hgb:Z + k = P + Q = ”Q Dr + k¦vm = D”Q¡vm

Giƒc: Pj”Qw³g D”Q…•Lj BZ¨vw`|

4. Z& I `& Gi ci W& _vK‡j Z& I `& Gi ¯’‡j W& nq| †hgb:

Z& + h = Ç Dr + Wxb = DÇxb

5. Z& I `& Gi ci n _vK‡j Z& I `& Gi ¯’‡j `& Ges n&-Gi ¯’‡j a& nq| ‡hgb: Z& + n = ` + a =× Dr + nvi = D×vi

`& + n = `& + a = × c` + nwZ = c×wZ

6. Z& I `& Gi ci j& _vK‡j Z& I `& Gi ¯’v‡j j D”PvwiZ nq| †hgb: Z& + j =jø Dr + jvm = Djøvm

Giƒc: D‡jøL, DwjøwLZ, D‡jøL¨, Djø•Nb BZ¨vw`|

(L) 1. e¨Äb aŸwbmg~‡ni †h †Kv‡bv e‡M©i A‡Nvl AícÖvY aŸwbi ci †h †Kv‡bv e‡M©i †Nvl AícÖvY I †Nvl gnvcÖvY aŸwb wKsev †Nvl AícÖvY Zvje¨ aŸwb, (h > R), †Nvl AícÖvY Iô¨ aŸwb (e), †Nvl K¤úbRvZ `šÍg~jxq aŸwb (i) wKsev †Nvl AícÖvY Iô aŸwb (e) _vK‡j cÖ_g A‡Nvl AícÖvY aŸwb †Nvl AícÖvY iƒ‡c D”PvwiZ nq| h_v:

K& + `& = M& + `& evK + `vb = evM`vb

U& + h = W& + h lU + hš¿= lohš¿

Z + l = `& + N Dr + NvUb = D`NvUb

Z + h = `& + h Dr + †hvM = D‡`¨vM

Z + e = `& + e Dr + eÜb = DØÜb

Z + i = ` + i Zr + iæc = Z`ªæc

2. O, R, Y, b g c‡i _vK‡j c~eeZx© A‡Nvl AícÖvY ¯úk© aŸwb †mB eMx©q †Mvl ¯úk© aŸwb wKsev bvwmK¨ aŸwb nq| h_v:

K + b = MO + b w`K + wbY©q = w`Mwbb©q ev w`KwbY©q

Z& + g = `/ b + g Zr + g‡a¨ = Z`vg‡`¨ ev Zb¥‡a¨

jÿYxq: G iƒc †ÿ‡Î mvaviYZ bvwmK¨ e¨ÄbB †ewk cÖPwjZ| †hgb: Zr + gq = Zb¥q, g„r + gq = g„b¥q, RMr + bv_ = RMbv_ BZ¨vw`| G iƒc Dbœqb, DbœxZ, wPb¥q BZ¨vw`|

3. g Gi ci †Kv‡bv evMx©q aŸwb _vK‡j g aŸwbwU †mB e‡M©i bvwmK¨ aŸwb nq| †hgb: g + K = O + K kg& + Kv = k¼v

g& + U = T + P mg& + Pq = mÂq

g + Z = b + Z mg + Zvc = mšÍvc

Giƒc: wK¤¢yZ, m›`k©b, wKbœi, m¤§vb, mÜvb, mbœ¨vm BZ¨vw`|

`ªóe¨: AvaywbK evsjvq g&-Gi ci KÉ¨-eMx©q aŸwb _vK‡j g& ¯’v‡b cÖvqB O bv n‡q Aby¯^vi (s) nq| †hgb:mg& + MZ = msNZ, Ang& + Kvi = AnsKvi, mg + L¨v = msL¨v| Giƒc: msKxY©, msMxZ,, msMVb, msNvZ

4. g&-Gi ci AšÍt¯’ aŸwb h, i, j, e wKsev k, l, m, n _vK‡j g& ¯’‡j Aby¯^vi (s) nq| †hgb:

mg& + hg = mshg mg& + ev` = msev`

mg& + iÿY = msiÿY mg& + jvc = msjvc

mg& + kq = mqkq mg& + mvi = msmvi

mg& + nvi = msnvi

Giƒc: evisevi, wKsev, mseiY, ms‡hvM, ms‡hvRb, ms‡kvabg me©smnv, ¯^qseiv| e¨vwZµg : m¤ªvU (mg& + ivU)

5. P& I R& Gi c‡i bvwmK¨ aŸwb Zvje¨ nq| †hgb:

P& + b = P + T hvP& + bv = hvP&Tv, ivR + bx = ivÁx

R& + b = R + T hR& + b = hÁ

6. `& I a& Gi c‡i K, P, U, Z, c, L, Q , V, _ , d _vK‡j `& I a& ¯’‡j A‡Nvl AícÖvY aŸwb nq| †hgb: ` > Z Z`& + Kvj = ZrKvj a&> Z ÿza& + wccvmv=ÿzrwccvmv Giƒc: ürwc¤ú, Zrci, ZË¡ BZ¨vw`|

7. `& wKsev a&-Gi c‡i m& _vK‡j `& I a& ¯’‡j A‡Nvl AícÖvY aŸwb nq| †hgb: wec` + msKzj = wec`msKzj | Giƒc: Zrmg

8. l-Gi c‡i Z& ev _& _vK‡j, h_vµ‡g Z& I _ ¯’v‡b U I V nq| †hgb: K…l& + wZ = K…wó ll&+ _ = lô

9. we‡kl wbq‡g mvwaZ KZ¸‡jv mwÜ

Dr + ¯’vb = DÌvb mg + Kvi = ms¯‹vi, Dr + ¯’vcb = DÌvcb

mg& + K…Z = ms¯‹…Z, cwi + Kvi = cwi¯‹vi

Giƒc : ms¯‹…wZ, cwi®‹…Z BZ¨vw`|

10. KZ¸‡jv mwÜ wbcZ‡b wm× nq

Av + Ph© = Avðh© , ‡Mv + c` = †Mv®ú`, eb + cwZ = eb¯úwZ

e„nr + cwZ = e„n¯úwZ, Zr + Kvi = Z¯‹i, ci + ci = ci¯úi

gbm + Clv = gbxlv lU& + `k = †lvok, GK + `k = GKv`k

cZr + AÄwj= cZÄwj

weMm© mwÜ

ms¯‹…Z mwÜi wbq‡g c‡`i AšÍw¯’Z i& I m& A‡bK †ÿ‡Î D®§ aŸwb A_©vr M aŸwbiƒ‡c D”PvwiZ nq Ges Zv wemM© (t) iƒ‡c ‡jLv nq| i& I m& wemM© e¨Äb aŸwbgvjvi AšÍM©Z| †m Kvi‡b wemM© mwÜ e¨Äb mwÜ AšÍM©Z| e¯‘Z wemM© i& Ges m& Gi mswÿß iƒc| wemM©‡K `y fv‡M fvM Kiv n‡q‡Q : 1, i&-RvZ wemM© 2. m&-RvZ wemM©

1. i&-RvZ wemM© : i ¯’v‡b †h wemM© nq Zv‡K e‡j i-RvZ wemM©| †hgb: AYÍi- AšÍt, cÖvZi-cÖvZt, cybi-cybt BZ¨vw`|

2. m&-RvZ wemM© : m& ¯’v‡b †h wemM© nq Zv‡K m&-RvZ wemM© e‡j| †ghb: bgm&-bgt, cyim&-cit, wkim&-wkit, BZ¨vw`|

wemM© I ¯^‡ii mwÜ

A-aŸwbi ciw¯’Z (A‡Nvl D®§aŸwb) wem‡M©i ci A aŸwb _vK‡j A + t + A G wZ‡b wg‡j I-Kvi nq ‡hgb:

wemM© I e¨Ä‡bi mwÜ

1. A-Kv‡ii ciw¯’Z m&-RvZ wem‡M©i ci †Nvl AícÖvY I †Nvl gnvcÖvY e¨ÄbaŸwb, bvwmK¨ aŸwb wKsev AšÍ¯’ h, AšÍ¯’ e, i, j, n _vK‡j A-Kvi I m&-RvZ wemM© Dfq ¯’‡j I-Kvi nq| †hgb- wZit + avb = wZ‡ivavb, gbt + ig = g‡bvig, gbt + ni = g‡bvni, Zct + eb = Z‡cveb BZ¨vw`|

2. A-Kv‡ii ciw¯’Z i&-RvZ wem‡M©i ci DcwiD³ aŸwbmg~‡ni †Kv‡bvwU _vK‡j wemM© ¯’v‡b ÔiÕ nq| †hgb: AšÍ t + MZ = AšÍM©Z, AšÍt + avb = AšÍa©vb, cybt + Avq = cybivq, cybt + D³ = cybiæ³, Ant + An = Anin| Giƒc: cybR©b¥v, cybe©vi, cÖvZiæÌvb, AšÍfz©³, cybivwc, AšÍe©Zx© BZ¨vw`|

3. A I Av wfbœ Abœ ¯^‡ii c‡i wemM© _AK‡j Ges Zvi m‡½ A, Av, eMx©q †Nvl AícÖvY I †Nvl gnvcÖvY bvwmK¨ aŸwb wKsev h, i, j, e, n Gi mwÜ n‡j wemM© ¯’v‡b ÔiÕ nq| †hgb:

e¨vwZµg: B wKsev D aŸwbi c‡ii wem‡M©i m‡½ ÔiÕ Gi mwÜ n‡j wem‡M©i †jvc nq I wem‡M©i c~e©eZx© n«¯^ ¯^i `xN© nq| †ghb-wbt + ie = bxie, wbt + im = bxim BZ¨vw`|

4. wem‡M©i ci A‡Nvl AícÖvY wKsev gnvcÖvY Zvje¨ e¨Äb _vK‡j wem‡M©i ¯’‡j Zvje¨ wkk aŸwb nq, A‡Nvl AícÖvY wKsev A‡Nvl gnvcÖvY g~a©b¨ e¨Äb _vK‡j wemM© ¯’‡j g~a©b¨ wkk aŸwb nq, A‡Nvl AícÖvY wKsev A‡Nvl gnvcÖvY `šÍ¨ e¨Ä‡bi ¯’‡j `šÍ¨ wkk aŸwb nq| †hgb:

t + P/Q = k + P/Q wbt + Pq = wbðq wkit + †Q` = wki‡ñ`

t + U/V = l + U/V abyt + U¼vi=abyó¼vi wbt + Vzi = wbôzi

t + Z/_ = m + Z/_ `yt + Zi = `y¯Íi `y t + _ = `y¯’

5. A‡Nvl AícÖvY I A‡Nvl gnvcÖvY KÉ¨ wKsev Iô¨ e¨Äb (K, L , c, d) c‡i _vK‡j A ev Av aŸwbi ciw¯’Z wemM© ¯’‡j A‡Nvl `šÍ¨ wkk aŸwb (m&) nq Ges A ev ev e¨ZxZ Ab¨ ¯^iaŸwbi ciw¯’Z wemM© ¯’‡j A‡Nvl gya©Y¨ wkk& aŸwb (l) nqq| †hgb:

Giƒc: cyi¯‹vi, gb¯‹vgbv, wZi¯‹vi, PZz®ú`, wbõj, wb®úvc, `y®úÖvc¨, ewn®‹…Z, `y®‹…wZ, Avwe®‹vi, PZz‡®‹vY, evP¯úwZ, fv¯‹i BZ¨vw`|

cÖvZt + Kvj = cÖvZtKvj, gbt + Kó = gbtKó, wkit = cxov= wkitcxov|

wbt + ¯Íä = wbt¯Íä wKsev wb¯Íä| `yt + ¯’ = `yt¯’ wKsev `y¯’| wbt + ¯ú›` = wbt¯ú›` wKsev wb¯ú›`|

wKQz ¯^imwÜi D`vnviYt-

MZvbyMwZK=MZ+AvbyMwZK, cyiva¨ÿ=cyi+Aa¨ÿ, Afxó=Awf+Bó, cixÿv=cwi+Cÿv, cÖZxwZ=cÖZx+BwZ, mZxk=mZx+Ck, Dchy©³=Dcwi+D³, Dchy©cwi=Dcwi+Dcwi, Ab~w`Z=Aby+Dw`Z,

wngvjq=wng+Avjq,

we`¨vjq=we`¨v+ Avjq, gvÎvwaK¨=gvÎv+AvwaK¨, Rgv‡bv=Rgv+Av‡bv, iƒcvwj=iƒc+Avwj, ¯^vaxb=¯^+Aaxb, kkv¼=kk+A¼, ˆØcvqb=Øxc Avqb, iex›`ª=iwe+B›`ª, myax›`ª=myax+B›`ª, Afxc&mv=Awf+Bc&mv, giæ`¨vb=giæ+D`¨vb, eayrme=ea~+Drme,

wKQz e¨Äb mwÜi D`vnviYt-

w`MšÍ=w`K&+AšÍ, wYRšÍ=wYP&+AšÍ, GKQÎ=GK+QÎ, cwi”Q`=cwi+‡”Q`, cÖwZ”Qwe=cÖwZ+Qwe, Aby‡”Q`=Aby+‡Q`,

RM`xk=RMr+ Ck, lovbb=lU&+Avbb, Z`ewa=Zr+Aeax, m`&cvq=mr+Dcvq, we‡”Q`=we+‡Q`, wewQbœ=we+wQbœ,

cÖ”Q`=cÖ+‡Q`, Pjw”PÎ=Pjr+wPÎ, e¾vZ=e`&+RvZ,

Z‡ZvwaK=ZZt+AwaK, e‡qvwaK=eqt+AwaK, A‡avMwZ=Aat+MwZ, Z‡cveb=Zct+eb, B‡Zvg‡a¨=BZt+g‡a¨, m†ivei=mit+ei,

Î‡qv`k=Îqt+`k, wZ‡ivavb=wZit+avb m‡`¨vRvZ=m`¨t+RvZ, g‡bv‡hvM=gbt+‡hvM, g‡bvig=gbt+ig, g‡bvni=gbt+ni, h‡kvjvf=hkt+jvf, bxie=wbt+ie, bx‡ivM=wbt+‡ivM,

‡h wbqg Abymv‡i Zrmg k‡ãi b, Y‡Z cwiYZ nq , Zv‡K YZ¡ weavb e‡j |

wbqgvewj :-

Ü F, i , l Gi c‡i ÔYÕ nq| †hgb: FY, iY, fxlY, iYf~wg, fvlY BZ¨vw`|

Ü KZ¸‡jv k‡ã ¯^fveZB ÔYÕ nq | †hgb t evYx , gvwYK, jeY, gY, evwYR¨, exYv BZ¨vw`|

e¨wZµg t

PvYK¨, gvwYK¨ MY evwYR¨ jeY gY, †eYy exYv K¼Y KwYKv|

Kj¨vY †mvwYZ gwY ¯’vY~ ¸Y c~Y¨ †eYx, AYy dwY wecwY MwYKv|

AvcY jveY¨ evYx wbc~Y fwYZv cvwY, ‡MŠY †KvY fvY cY †MŠY lvY

wP°Y wbK¡Y Z…Y ZzY kvwY ewYK ¸Y, MYYv weYvK cY¨ evY

‡h wbqg Abymv‡i Zrmg k‡ãi m, l-‡Z cwiYZ nq, Zv‡K l-Z¡ weavb e‡j |

wbqgvewj t

Ü A, Av wfbœ ¯^iaŸwb Av‡M _vK‡j mvaviYZ ÔlÕ nq| †hgbt welq, wel, Pÿz®§vb BZ¨vw`|

Aby + m½ > Abyl½, my + mg> mylg, Awf + †mK > Awf‡lK|

Ü KZ¸‡jv k‡ã ¯^fveZB ÔlÕ nq| †hgb t gvbyl , mwilv, fvlv, †Kvl, †cŠl , †Øl, Avlvp, †lvok BZ¨vw`|

e¨wZµg t

Ü we‡`wk k‡ãi mv‡_ KL‡bvB ÔlÕ nq bv| †hgb t †cvkvK, †÷kb , gv÷vi , Wv÷vi BZ¨vw`|

Ü k‡ãi †k‡l ÔmvrÕ cÖZ¨q hy³ _vK‡j ÔlÕ nq bv| †hgb t AvZ¥mvr , AwMœmvr, a~wjmvr BZ¨vw`|

wbcZ‡b wm× -l-Gi e¨envi wewa:

wekvY †kvlY wel cy®ú †`vl †ivl , kwnl Avi g~wlK ewj cyiæl cÖ‡`vl

cÖZz¨l f~lY †Kvl fzlv k®ú †kl, ev®ú lU fvl¨ †cvl¨ wfjvl †kl|

Av‡jvP¨ welq- wj½

(K) cyswj½ (L) ¯¿xwj½

(M) Dfqwj½ (M) K¬xewj½

(K) cyswj½ t- ‡h kã Øviv c~iæl RvwZ ‡evSvq, Zv‡K cyswj½ e‡j| †hgb- evev, fvB, wcZv, PvPv, KvKv, cyÎ BZ¨vw`|

(L) ¯¿xwj½t- ‡h kã Øviv ¯¿x RvwZ ‡evSvq, Zv‡K ¯¿xwj½ e‡j| †hgb-gv, †evb, Lvjv, ivwb, †g‡q BZ¨vw`|

(M) Dfqwj½t- ‡h kã Øviv cyiæl I ¯¿x `yB †evSvq, Zv‡K Dfqwj½ e‡j| †hgb-wkï, mv_x, Avwg, Miæ, gvbyl BZ¨vw`|

(M) K¬xewj½t- ‡h kã Øviv cyiæl I ¯¿x wKQzB †evSvq bv, Zv‡K K¬xewj½ e‡j| †hgb-e„ÿ, dzj, Kjg, `vjvb, mwgwZ BZ¨vw`|

wKQz wbZ¨ cyiælevPK kãt- wKQz evsjv kã Av‡Q hv Øviv ïay cyiælevPK †evSvq-‡hgbt KweivR, †hv×v, †XKx, AK…Z`vi, cy‡ivwnZ, ‰¯¿Y, ‡Kivwb BZ¨vw`|

wKQz wbZ¨ ¯¿xevPK kãt- wKQz evsjv kã Av‡Q hv Øviv ïay ¯¿xevPK †evSvq, G¸‡jvi †Kvb cyiælevPK kã nq bv| ‡hgbt mZxb, mcZœx, maev, mrgv, WvBwb,Aa©w½bx, AšÍ¯^Ë¡v, Amyh©¤úk¨v AiÿYxq, Kjw¼bx, evBwR, KzjUv, kvwLbx, G‡qv, `vB, BZ¨vw`|