সংজ্ঞা : মাত্রা, ফাঁক, লয়, সম, দ্বিগুণ, চারগুণ, আড়ি, বাদী, সমবাদী, আরোহন ও অবরোহন

            gvÎv

          Zv‡ji ¶z`ª ¶z`ª Ask hv jq‡K cwigvc K‡i ZvÔ‡K gvÎv e‡j|

gvÎv n‡”Q Mvb MvB‡Z wKsev hš¿ msMx‡Z Mr evRv‡Z †M‡j Mv‡bi ev Mr-Gi cÖ‡Z¨K ¯^i KZ¶Y ¯’vqx n‡e Zv Rvbevi Rb¨ mv‡¼wZK wPý| msMx‡Z GK GKwU ¯^‡ii Kvj‡K gvÎv e‡j|

          gvÎvi mg‡qi cwigvY Av‡Q| c„w_exi mg¯Z cÖvYxB gvÎvi  Aaxb| gvÎv hLb †_‡g hv‡e ZLb mg¯Z cÖvYxi wµqv eÜ n‡q hv‡e| †hgb Nwoi †cÛyjvg hZ¶Y wUK wUK kã Ki‡e ZZ¶Y Nwoi cÖvY Av‡Q| gvbyl I RxeRš‘i agwb hZ¶Y ¯úw›`Z n‡e ZZ¶Y †m RxweZ _vK‡e| MvbevRbvI Z`ªyc| †hgb gvÎv eÜ Agwb m‡½ m‡½ Mvb evRbvI eÜ n‡q hv‡e| g„Zz¨i mgq gvÎv eÜ n‡j Kvj G‡m wb‡q hvq| GB Kvi‡Y g„Zz¨i Aci bvg n‡”Q Kvj| gvby‡li agwbi ac& ac& kã Avi Nwoi wUK wUK kã‡K GK gvÎv wn‡m‡e aiv ‡h‡Z cv‡i| Av‡iv wKQy gvÎvi bvg Av‡Q †hgb Aa©gvÎv, wmwK gvÎv ev wewfbœ Zv‡j wewfbœ gvÎvi wgjb †`Lv hvq| eZ©gv‡b Avgv‡`i †`‡k ¯^‡ii ci GKwU Av (v) Kvi †hvM K‡i GK gvÎv Ges t (wemM©) †hvM K‡i Aa© gvÎv Avi 0 (k~b¨) †hvM K‡i wmwK gvÎv cÖKvk Kiv nq|

‡hgb t GK gvÎvi ¯^i = m    i    M    g    c    a    b    m©

Aa© gvÎvi ¯^i   = tm    ti    tM    tg    tc    ta    tb    tm©

wmwK gvÎvi ¯^i          = 0m    0i    0M   0g    0c    0a    0b    0m©

duvK

          Zv‡ji †evj ev evYxi †h wefv‡M n¯Z cÖ`k©Y Kiv n‡q _v‡K Ges nvZ w`‡q Zvwj bv w`‡q ïay AvNvZ k~Y¨ †mB ¯’vb‡K dvuK ev Lvwj ejv nq| dvuK‡K Ô 0 Õ wPý w`‡q cÖKvk Kiv nq|

mg

‡Kvb Zv‡ji evYx ev gvÎvi cÖ_g AvNvZ‡KB mg e‡j| mg‡K Ô+Õ wPý w`‡q cÖKvk Kiv nq| mg Zv‡ji GKwU ¸iyZ¡c~Y© ¯’vb| KviY mg †_‡KB Zv‡ji ïiy Ges m‡g G‡mB Zvu‡ji †kl|

ev`x ¯^i

          iv‡M e¨eüZ ¯^‡ii g‡a¨ †h ¯^iwU AZ¨waK †ewk e¨envi Kiv nq A_©vr †h ¯^i‡K cÖvavb¨ †`qv nq †ewk Zv‡K ev`x ¯^i ev cÖavb ¯^i ejv nq|

          ev`x ¯^i A_© cÖavb ev gyL¨ ¯^i| iv‡Mi ev`x A‡_© iv‡Mi e¨eüZ ¯^i¸wji g‡a¨ cÖavb ¯^iwU‡KB †evSvq| A_©vr ¯^i¸wji g‡a¨ †h ¯^iwU cÖvavb¨ jvf K‡i A_ev †h ¯^iwU‡K cÖvavb¨ †`Iqv nq †mB ¯^iwUB iv‡Mi ev`x ¯^i|  kv¯¿g‡Z cÖwZwU iv‡MB †Kv‡bv bv †Kv‡bv GKwU ¯^‡ii cÖvavb¨ _v‡K| evievi e¨envi K‡i AwaK¶Y ¯’vqx  ev wekªvg (b¨vm) K‡i A_ev Ab¨ †KvbiKg mv½xwZK AvjsKvwiK wµqvi Øviv †SvuK ev †Rvi w`‡q †h ¯^iwU‡K †Kv‡bv GKwU iv‡M cÖej K‡i †`Lv‡bv nq, †mB ¯^iwUB iv‡Mi ev`x ¯^i| ev`x - ¯^iB iv‡Mi Rxeb| cwðgv‡j ev`x- ¯^i‡K PjwZ K_vq ZvB ÔRvbÕ ev ÔRxeb-¯^iÕ e‡j| m½xZiv‡R¨ ev`x-¯^‡ii m¤§vb ivRZzj¨|

mgev`x ¯^i

          ev`x ¯^‡ii c‡i †h ¯^iwU wKQy Kg e¨envi nq Zv‡K mgev`x ¯^i e‡j| A_v©r ev`x ¯^‡ii c‡iB mgev`x ¯^‡ii ¯’vb| m½xZiv‡R¨ mgev`x ¯^‡ii m¤§vb cÖavbgš¿xZzj¨|

          cÖKvk, Av‡ivnx-Ae‡ivnxi ciB ivM MV‡b Ges ¯^iƒc cÖKv‡k ev`-mgev`x ¯^i `ywUi ¸i“Z¡ me©vwaK| G‡`i e¨envwiK ixwZi DciB iv‡Mi †mŠ›`h© wbf©i K‡i| G Qvov mg¯^iwewkó ivM¸wj GKwU Ab¨wU n‡Z c„_K nq ïay ev`x-¯^i A_ev ev`x-mgev`x Dfq ¯^i `ywUi cwieZ©‡b| †hgb f~cvjx I †`kKvi, av‡bkªx I fxgcjkªx BZ¨vw`| iv‡Mi ev`x-mgev`x ¯^i `ywU mvaviYZ loR-ga¨g A_ve loR-cÂg fve| A_©vr Ômv-gvÕ A_ev Ômv-cvÕ e¨eav‡b Aew¯’Z nq| kÖywZ wn‡m‡e beg A_ev ·qv`k kÖywZ¯’v‡b Aew¯’Z nq| wKš‘ ivMwe‡k‡l Gi e¨wZµgI N‡U‡Q| †hgb - kªxivM|

Av‡ivnb I Ae‡ivnb t

          wbw`©ó GKwU ¯^i‡K ÔmvÕ a‡i µgvš^‡q Dc‡ii w`‡K evwR‡q Zvivi ÔmvÕ ch©šZ hvIqv‡K Av‡ivnY ev Av‡ivnx e‡j |

          Zvivi ÔmvÕ n‡Z wb‡Pi w`‡K evwR‡q wbw`©ó ÔmvÕ ch©šZ AeZi‡Yi bvg Ae‡ivnb ev Ae‡ivnx|

¯^i

          RxeRš‘ cÖf„wZi KÉ n‡Z Ges †Kv‡bv c`v‡_©i AvNv‡Z †h cÖKvi kã ev AvIqvR nq Zv‡K ¯^i ejv nq| wKš‘ †mB ¯^i hLb m½xZ Dc‡hvMx nq A_©vr kªe‡Y wPË cÖmbœ nq ZLbB Zv‡K cÖvK…wZK m½x‡Zi ¯^i ejv nq | wewfbœ hš¿vw` n‡Z wbM©Z aŸwb‡K myi ejv nq| ‡hgb - evuwki myi, †envjvi myi BZ¨vw`|

          evsjv fvlvq †hgb 12wU ¯^ieY©, 48wU e¨ÄbeY© Av‡Q| Bs‡iRx‡Z 26wU eY© ev A¶i I Aviwe‡Z 30wU nid Av‡Q, ms&Mx‡ZI †Zgwb 7wU gvÎ ¯^i Av‡Q| †hgb- loR, Flf, MvÜvi, ga¨g, cÂg, ˆaeZ I wblv`| PjwZ K_vq loR, Flf I wblv`‡K h_vµ‡g LiR, †iLve I wbLv` ejv nq|

          ‡Kv‡bv GKwU wbw`©ó myi‡K ÔmvÕ a‡i wb‡q H mv n‡Z †i, †i n‡Z Mv, gv n‡Z cv, cv n‡Z av Ges av n‡Z wb ¯^i¸wj c~Y©všZ‡i (GKwU ev‡` GKwU iƒ‡c) Aew¯’Z n‡j †mB ¯^i¸wj nq ï× ¯^i Ges cÖwZ `ywU ï× ¯^‡ii ga¨Kvi ev` †`Iqv Aa©všZ‡i Aew¯’Z ¯^i¸wj nq weK…Z ¯^i| wKš‘, ï× Mv I gv Ges ï× wb I mv© ¯^i `ywU cvkvcvwk Aa©všZ‡i Aew¯’Z| ‡Kvgj ¯^i n‡jv Pvi (4) wU I Kwo ¯^i GK (1)wU| ‡Kvgj ¯^i¸‡jv n‡jv F, Á, `, Y Ges Kwo ¯^i n‡jv Kwo Ô¶Õ | †gvU ¯^i n‡jv 12wU|

jq

          MxZ ev‡`¨i mg‡qi I Q›` fw½i mgZv‡K jq e‡j| jq n‡jv †h †Kv‡bv Zv‡ji MwZ, GB MwZ‡KB jq e‡j| Nwoi wUK wUK kãI GKwU j‡q Pj‡Z _v‡K| jq wZb cÖKvi| †hgb- wejw¤^Z jq, ga¨ jq I `ªyZ jq|

wejw¤^Z jq, A_©vr ax‡i ax‡i| ga¨ jq n‡”Q wejw¤^Z j‡qi †P‡q wظY `ªyZ| Avevi ga¨j‡qi wظY `ªyZ‡K `ªyZ jq e‡j| Gi c‡i Av‡¯Z Av‡¯Z †PŠ`ywb jq n‡Z cv‡i| 

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