Bcy-`-Sobw þ Hcp \qX-\-hym-Jym-\hpw Is−¯epIfpw sI.N{µlcn 1. BapJw imkv{X-¯nsâ ]pcm-X-\hpw B[p-\n-I-hp-amb Ncn-{X-¯n shÅn\£{Xw t]mse tim`-bmÀ¶ \ma-amWv Bcy-`-S³. imkv{XNcn{XImc-·m-cpsS a\-Ên Ime-¯nsâ ]n¶m-¼p-d¯p \n¶pw HmSnsb-¯p¶ biz-kn-I-fmb {]Xn-`-IÄ¡v Gähpw ap¼n AZzn-Xo-b-amb aln-a-tbmsS \ne-sIm-Åp¶ `mc-Xob imkv{XÚ-\mWv Bcy-`-S³. B[p-\n-I-Im-e-¯n\v Bcy-`-S-tâ-Xmbn e`y-am-bn-cn-¡p-¶ GI IrXn \qän-bn-cp-]Xv tÇmI-§Ä am{X-apÅ Bcy-`-SobamWv. F¶m {InkvXp-hn\v tijw Bdmw -\q-äm−v apX-epÅ `mc-Xob tPymXnx-imkv{X {KÙ-§-fn-seÃmw Bcy-`-S-s\-¸än ]cm-aÀihpw `mkvI-cm-Nm-cyÀ H¶m-asâ Imew ({In-kvXp-hÀjw 628) apX Bcy-`-So-bm-[n-jvT-amb Hcp tPymXnx-imkv{X-]m-c-¼-cyhpw `mc-X-¯n \ne-\n¡p-¶p. temI¯v asämcp imkv{XÚ\pw e`n-¡m¯ \nkvXp-e-amb A`n-\-µ\w Ignª H¶c kl-{km-_vZ¯n Bcy-`-S\v kn²-am-Wv. Bcy-`-Ssâ A\ym-Zr-i-amb Cu {]i-kvXn-bpsS Imc-W-sa-´mWv? ]Xn-s\«mw \qäm-−n ]©-kn-²m-´n-I¡v BwK-e-]-cn-`mj \ÂInb ]mÝm-Xy-\mb Pn.-Xn-t_m-«ns\ Bcy-`-Ssâ JymXnbmWv AXn-i-bn-¸n¨-sX-¦n Ccp-]-s¯m¶mw \qäm-−n Ata-cn-¡³ `uXnIimkv{X-Ú-\mb sU¶nkv Uyq¡ns\1 AXn-i-bn-¸n-¨n-cn-¡p-¶Xv Bcy-`-So-b-¯nse {Kl-a-[y-a§-fpsS AXo-h-kq-£va-X-bm-Wv. 'Hcp C´y³ \nKq-VX' F¶ Xsâ ]T-\¯n Uyq¡v Ignª c−v \qäm−v Imes¯ \nc-h-[n-]-T-\-§sf Ah-temI\w sNbvXv, hnaÀi-\-§sfbpw A`n-\-µ-\-§-sfbpw ]cn-tim-[n¨ tijw Bcy-`-Ssâ AXn-i-bn-¸n-¡p¶ IrXyX, FÃm hnaÀi\§-sfbpw Akm-[phm¡p¶ Hcp \nKq-V-X-bm-sW¶ \nK-a-\-t¯m-sS-bmWv Ah-km-\n-¡p-¶-Xv. Bcy-`-S-s\-¸-än-bpÅ ]mÝm-Xy-]-T-\-§-fpsS Ncn{Xw Bcw-`n-¡p-¶Xv tUm. F¨v. sI¬2 tdmb Gjym-änIv skmssk-än-bpsS tPÀW-en {InkvXphÀjw 1863  {]kn-²o-I-cn¨ ]T-\-t¯m-sS-bm-Wv. C³tUm-f-Pn-Ìmb tImÄ{_q¡ns\ Xmsg-¡m-Wpw- hn[w D²-cn-¨p-sIm-−mWv sI¬ Xsâ ]T\w Bcw-`n-¨n-cn-¡p-¶-Xv. "(Bcy-`-S³) _oP-K-WnXw BZy-ambn Ah-X-cn-¸n-¡p¶ `mc-Xob imkv{XÚ³ þ Hcp ]s£ XoÀ¯pw kzIo-b-am-b-Xà F¶v Icp-Xn-bm Xs¶ \nÝb-ambpw e`y-amb Úm\s¯ Xsâ A\n-X-c-km-[m-c-W-amb {]Xn-`- sIm−v
1
Dennis W. Duke, Professor of Physics, Florida State University: 'An Indian Mystery' scheduled to appear in DIO Journal. 2 Dr. H. Kern, On Some Fragments of Āryabhata, 16 March 1863, Journal of the Royal Asiatic Society.
1
sa¨-s¸-Sp-¯n-sb-Sp-¯-Xm-Wv. -`mc-X-¯n KWn-X-¯n\v kn²-amb D¶-Xn-bpsS Gähpw sa¨-amb {]I-S-\-amWXv" tImÄ{_q-¡n-sâbpw sIWn-sâbpw A`n-\-µ-\-§-tfmsS Bcw-`n¨ ]mÝmXy]T\-§Ä a\p-jy³ N{µ-\n-se-¯n-b-Xn\v tijw `mcXob imkv{X-Ú-·mÀ Nm{µ-bm\w kz]v\w ImWp¶ Cu I¼yq-«À bpK-¯nepw imkv{X-Im-c-·m-cpsS hnkva-b-ambn \ne-sIm-Åp-¶p-sh¶v Uyq¡nsâ ]T\hpw ap³]-dª \nK-a\hpw kqNn¸n¡p-¶p. Bcy-`StâXmbn Adnbs¸Sp¶ c−v {]kn²amb IrXnIÄ BcymÀ²cm{X kn²m´w, BcyuZbnIkn²m´w ChbmWv. Chbn HuZbnI]£w F¶v {]kn²amb Bcy`Sobw am{Xta ]qÀ®ambn C¡me¯v e`yambn«pÅp. BÀ²cm{X]£w `mkvIcmNmcyÀ H¶masâ D²cWnIfn \n¶pw {_ÒKp]vXsâ (CE 628) JWvUJmZyIsa¶ _Ôs¸« IcW{KÙ¯n \n¶pamWv a\Ênem¡phm³ Ignbp¶Xv. Bcy`Ssâ {]amW§Ä, IrXnIÄ Ch kw_Ôn¨v {_Ò Kp]vXsâ Imew apX Xs¶ ]e hnhmZ§fpw {]kn²§fmWv. `mkvIcmNmcyÀ H¶ma³ (CE 629) AivaIobs\¶v hntijWw \ÂIp¶psh¦nepw Imem´c¯n AivaIw FhnsSsb¶v Xn«anÃmsX hcnIbm At±l¯nsâ kztZihpw {KÙ§fn \nÝnXamb ]cmaÀianÃm¯Xn\m Imehpw ]n¡me¯v hnhmZhnjb§fmbn. Bcy`Ss\ Gähpw {it²b\m¡p¶ kwKXn At±lw Xsâ kw£n]vXamb {KÙ¯neqsS `mcX¯n\v Nn«s¸Sp¯n \ÂInb imkv{XobXbpsS cmPþ ]mXbmWv. tPymXnx-im-kv{X-¯nsâ temI-N-cn-{X-¯n Xs¶ hnj-bs¯ KWn-Xw, Ime-{In-b, tKmfw C§s\ thÀXncn-¡p-Ibpw KWn-Xs¯ {]tXy-Iamb Hcp A²ym-b-am¡n Ah-X-cn-¸n-¡p-Ibpw sNbvX BZy tPymXn-Èm-kv{XÚ\pw KWn-X-Ú\pw At±-l-am-Wv. Bcy-`-Sob-¯nsâ imkvXob LS-\bpw kw{K-lW kz`m-hhpw Gähpw B[p-\n-I-amb imkv{X-{]-_-Ôc - -N-\m-co-Xnsb Xs¶ shÃpw-hn[w Imem-Xo-X-ambn \ne-sIm-Åp-¶p. Xnt_m-«nsâ hm¡p-IÄ IS-sa-Sp¯p ]d-ªm `mc-Xo-b-K-Wn-X-im-kv{X-s¯bpw hntZ-i¯v \n¶v e`n¨ JtKm-fo-b-K-Wn-X-hn-Úm-\-s¯bpw ka-\z-bn-¸n¨v tPymXnx-im-kv{X-kn²m-´-§Ä¡v hyàhpw Nn«-bp-ap-Å-Xp-amb cq]w \ÂIn hymJym-\n¨ BZy `mc-Xo-b-im-kv{X-Ú-\mWv Bcy-`-S³. Bcy`Ssâ ØeIme§Ä, IrXnIÄ Chsb Npän¸än \n¡p¶ AhyàXIsfbpw hnhmZ§sfbpw hniZambn ]cntim[n¡m\pÅ Hcp {iaamWv Cu ]T\w.
2. Cu ]T-\-¯nsâ ]Ým-¯ew kzX-{´-`m-cX¯nsâ Adp-]Xmw hÀj-¯nepw `mc-Xo-b-im-kv{X-N-cn-{X-Im-c-·mÀ Bcy-`-S-s\-¸-änbpw Bcy-`-So-b-s¯-¸-änbpw Aim-kv{Xo-b-amb [mc-W-IÄ ]peÀ¯n-¡mWp¶ A\p-`-h-amWv Cu ]T-\-¯n\v t{]c-I-ambn `hn-¨-Xv. C´y³ \mj-W kb³kv A¡m-Z-an- {]kn-²o-I-cn¨ ]e IrXn-I-fnepw CXc tPÀW-ep-I-fn {]kn-²o-Ir-X-ambn ImWp¶ ]T-\-§-fnepw Xmsg-¸-d-bp¶ sshI-ey-§Ä Zriy-am-Wv.
2
1.
Bcy-`-So-b-¯nsâ Ic-Wm-cw`w KX-Ien 3600 (499CE3) BIp-¶p. Cu [mcW icn-b-Ã. kuc-hÀj-am\w A\p-k-cn¨v BcymÀ²-cm-{X-kn-²m-´¯nsâ Ic-Wm-cw-`-amWv KX-Ien 3600. Bcy`-So-b-¯n\v Ic-Wm-cw`w tIcfo-b-]m-c-¼-cy-¯nÂ, lcn-Z-¯³ (\m-dm-W¯v {`m´³) \ÂInb hymJym-\a-\p-k-cn¨v KX-Ien 3623 (CE 522) Ic-Wm-cw-`-am-Ip-¶p. KWn-X-]-c-ambpw4 {KÙ-tc-J-IÄ hgnbpw Cu hkvXpX kn²-am-sW-¦nepw {]N-en-X-am-bn-cn¡p¶ Øqe-]-£-§Ä imkv{X-tem-I¯v ta[m-hnXzw ]peÀ¯n-¡m-Wp¶p. tIc-fob ]mc-¼-cy-¯n tPyjvT-tZ-h-tâ-Xmbn Icp-Xs - ¸-Sp¶ Zr¡-cW-¯n lcn-Z-¯-hym-Jy\w þ Kncn-Xpw-tKXn Iey_vtZ KWnXw \nÀ½nXw ]cw imkv{Xw Bcy-`-So-bmJyw... þ F¶v tcJ-s¸-Sp-¯n-¡m-Wp-¶p. KncnXpwKw IS-]-bmZn kt¦-X-a-\p-k-cn¨v KX-Ien 3623 BIp-¶p.
2.
`mcXobimkv{XNcn{X¯nse Gähpw k¦oÀ®amb AhyàXIfnsem ¶mWv Bcy`Ssâ tZiw. sFXnly§fpw Bcy`Sob¯ne[njvTamb tIcf ¯nse tPymXnximkv{X ]mc¼cyhpw Bcy`S³ tIcfob\msW¶ [mcW¡v _ew \ÂIpt¼mÄ Ipkpa]ptc`yÀ¨nXw Úm\w F¶ BNmcy ]cmaÀi ¯m Xs¶ At±lw Ipkpa]pchmknbmbncp¶p F¶ \nKa\¯n\v KthjIÀ km[pX IÂ]n¡p¶p. Ncn{X KthjW¯nsâ Ignª \qäm−nte¡v Xncnªp t\m¡nbm ImWp¶Xv þ
B[p\nItKhjW§fpsS BZyIme¯v tIcfob]mc¼cyw Bcy`Sobm[n jvTamsW¶ hkvXpX ASnØm\ambpw hymJymXm¡Ä an¡hcpw tIcfobcmsW¶Xn\mepw Ncn{X ]WvUnX·mÀ Bcy`S³ tIcfob\msW ¶ [mcW ]peÀ¯nbncp¶p. `mkvIcmNmcyÀ H¶mas\¸än kp[mIcZznthZn, i¦À _meIrjvWZo£nXv apXemb {]NWvU ]WvUnX·mÀ¡v AdnhnÃmXncp¶ Imeambncp¶p CXv. ]n¡me KthjW§Ä `mkvIcobNcn{Xw shfnhm¡nbt¸mÄ Bcy`S³ AivaI\msW¶pw AivaIw FhnsSbmsW¶papÅ At\zjWw Bcw`n¨p. B]vtXbpsS kwkvIrX\nLWvUp ASnØm\ambn AivaIw XncphnXmwIqdmsW¶ k¦Â]w XpSÀ¶v {]Ncn¡pIbp−mbn. XpSÀ¶v h¶ kzmX{´ym\´c ZiI§fn _u²þssP\tcJIÄ Bkv]Zambn AivaIw tKmZmhcn¡pw \À½Z¡panSbnepÅ hmImSIcmPy¯nsâ `mK ambncp¶psh¶ [mcW iàamIpIbpw Bcy`S³ A§s\ Ipkpa 3
CE 499, {InkvXp-hÀj-¯n\v Common Era F¶v \ÂIn-bn-cn-¡p¶ B[p-\nI \mam-´-c-¯nsâ Npcp-¡-amWv CE Bbn \ÂIp-¶-Xv.
4
K.Chandra Hari, Genesis and Antecedents of Aryabhatiya, IJHS 37(2), 2002, pp.101-113, Bcy-`-So-b-s¯-¸än Xncp-h-\-´] - p-c¯v \S¶ knt¼m-kn-b-¯nÂ
Ah-X-cn-¸n¨ {]_Ôw ]n¶oSv Indian Journal of History of Science  {]kn²o-I-cn-¨-p.
3
]pct¯¡v t]mb almcmjv{S kztZinbmsW¶ Nn´ _es¸SpIbpw sNbvXp. Cu ]Ým¯e¯n C´y³ \mjW kb³kv A¡mZanbpsS HutZymKnI {]kn²oIcW§Ä Xs¶ XoÀ¯pw hyXykvXamb ImgvN ¸mSpIfmWv DÄs¡mÅp¶Xv. s{]m^. Ir]mi¦À ip¢bpsS Bcy`Sob¯nsâ BwKe]cn`mjbn Bcy`S³ Ipkpa]pchmknbpw AivaIob\pamsW¶pw AivaIw hmImSI P\]ZamsW¶papÅ [mcW {]Ncn¸n¡p¶p. imkv{Xw C´ybn F¶ `mcX¯nse imkv{XNcn{X kw_Ôamb {]kn²oIcWw hyXykvXambn Bcy`S³ tIcfob\msW¶ [mcW ]peÀ¯p¶p. F³sskt¢m]oUnb {_n«m\n¡, CXc A´Àt±iob {]kn²oIcW§ Ä, sh_vsskäpIÄ, apXembh Cu HutZymKnI {]kn²oIcW§sf B{ibn¨v ]ckv]cw sshcp²yamÀ¶ hnhc§Ä Bcy`Ss\¸än \ÂIp¶p. Bcy`Ssâ IcWmcw`w Ien 3623 (iI 444) AYhm {InkvXphÀjw 522 BsW¶ tIcfob]mc¼cy¯n\pw aXnbmb AwKoImcw Ncn{XImc·mÀ \ÂIn ImWp¶nÃ. sFXnly§fpw sImSp§ÃqÀ sImSpwIÃqÀ (AivaIw) BsW¶ Dulm t]mlhpw am{XamWv tIcfob]mc¼cy¯n Bcy`Ss\ kw_Ôn¨v e`yambncn¡p¶ hnhc§Ä. sImSp§ÃqÀ sImSpwtImeqÀ Bbncp¶p sh¶v kqNn¸n¡p¶ XanÄ tcJIÄ Cu Nn´mKXnsb \ncmIcn¡phm³ tUm. sI. hn. iÀ½sbt¸msebpÅ KthjIsc t{]cn¸n¨Xn\memWv Ipkpa]pchmknbmbn Bcy`S³ C´y³ \mjW kb³kv A¡mZan bpsS Bcy`Sob¯n Nn{XoIcn¡s¸«Xv. tIc-fob tPymXnx-im-kv{X-]m-c-¼-cy-¯nsâ alna shfn-¨¯p sIm−p-h-cm³ Xsâ Pohn-X-Imew apgp-h³ A£oWw ]cn-{i-an¨ Kth-j-I-\mb tUm.-sI.hn.-iÀ½¡v Xs¶ Bcy-`-Ssâ tIc-fo-b-]m-c-¼cyw \ntj-[n-¡p-hm³ t{]c-Iamb kml-Ncy§fmWv `mc-X-¯nse B[p-\nI Kth-jW sshI-ey-§Ä krjvSn-¨-Xv. "Bcy`Ssâ \maw, Imew, tZiw"5 F¶ teJ-\-¯n (2001) tIc-f-¯n {]N-cn-¨n-cp¶ Aim-kv{Xo-b-amb [mc-W-Isf At±lw kaqew \ntj-[n-¡p-I-bp-−m-bn. 1. sImSp-§-ÃqÀ = sImSpw-I-ÃqÀ = Aiva-Iw F¶ hymJym\w icn-b-söpw Bcy-`-Ssâ Ime-amb Bdmw \qäm-−n sImSp-§-ÃqÀ sImSpw-sIm-eqÀ Bbn-cp¶p-sh¶pw tcJ-I-fp-²-cn¨v At±lw Øm]n-¡p-I-bp-−m-bn. 2. Bcy-`-So-b-¯nsâ `mjy-Im-c-·m-scÃmw tIc-fo-b-cm-sW¶ hmZhpw Ig-¼n-Ãm-
¯-Xm-sW¶v sXfn-hp-IÄ klnXw hyà-am-¡n. {]`m-I-c³, `mkvI-c³ (h-Ã-`n, KpP-dm-¯v), tkmta-iz-c³ (Kp-P-dm-¯v), kqcy-tZ-h³ (]qw-]p-lmÀ), bÿ (B{Ô), cLp-\m-Y-cm-P³ (A-tlm-_new IÀ®m-S-Iw), am[-h-þ-hn-cq-]m-£³ (B{Ô), `qXn-hn-jvWp-þ-tZ-h-cm-P³ (Im-©o-]p-cw), tImZ-WvU-cm-a³ (B-{Ô) C§s\ tIc-f-¯n\v shfn-bn \n¶pÅ `mjy-Im-c-·m-cp-sSbpw eÃm-Nm-cyÀ, 5
KV Sarma, "Āryabhata, His Name, Time and Provenance", Indian Journal of History of Science, December 2001, 105-115.
4
{_Ò-tZ-h³, Zmtam-Z-c³ (`-S-Xp-eyImc³), hoc-knw-l-K-W-I³ (B-cy-kn-²m-´Xp-ey-I-c-Ww) XpS-§nb Bcy-`-S]mc-¼-cy-¯n kwPm-X-amb kzX-{´-Ir-Xn-IfpsS tIc-fo-b-c-Ãm¯ IÀ¯m-¡-·m-sc¸änbpw tUm. iÀ½ kqNn-¸n-¡p-¶p. `mkvI-c³ H¶m-asâ ka-Im-en-I-\mb {_Ò-Kp-]vXsâ hnaÀi-\hpw ]n¡m-e¯p-−mb B-cymÀ²cm{X-kn-²m-´-Xp-eyamb JWvU-Jm-ZyI-I-c-Whpw Gsd {]kn-²-am-Wv. 3. Ipkp-a-]p-cw, ]pjv]-]pcw Fs¶ms¡
Adn-b-s¸« Øew ]mS-eo-]p-{X-amsW¶v ]I t]mse Ncn-{X-tc-J-I-fn \n¶pw hyà-am-bn«pw XrÈq-cnse ]q¦p¶s¯ Ipkp-a-]p-c-am-¡p¶ Kth-j-W-s¯bpw XanÄ\m-«ns\ Aiva-Ihpw ]qw]p-lm-dns\ Ipkp-a-]p-c-am-¡p¶ hmZ-s¯bpw At±-la ]mtS \ncm-I-cn-¡pI-bp-−m-bn. Bcy-`-Ssâ tIc-fo-b-]m-c-¼cyw A_-²-P-Sn-e-amb sFXn-ly-am-sW¶ \nK-a\w imkv{X-tem-I¯v {]N-cn-¡p¶ Ccp-]-s¯m¶mw \qäm-−nsâ Cu ]Ým-¯-e¯n-em-Wv Hcp ]pXnb At\z-j-W-¯n\v ChnsS Hcp-s¼-Sp-¶X - v. ]Xn\©p \qäm−pIfpsS tIcfob ]mc¼cyhpw B[p\nI KthjW§fpsS c−v \qäm−pIfpw AhyàX ]peÀ¯pt¼mÄ, Hcp ]pXnb At\zjW¯n\v km[yXIÄ IpdhmWv. ]gb teJ\§fnse Dulmt]ml§sf Xncn¨pw adn¨pw amänsbgpXpItbm, Ahsb hmNmeambn AhXcn¸n¨v tIcfob tPymXnximkv{X ]mc¼cy¯n\v AÂ]w IqSn [hfna ]IcpItbm Aà ChnsS e£yw. Bcy`Sobw ASnØm\ambn \S-¯nb Hcp imkv{Xob]cy-th£-W-¯nsâ Cw¥o-jv tPÀW-ep-I-fn {]kn-²-amb {]_-Ô-§-fpsS Hcp kw{K-lnXcq]w ae-bm-f-¯n Ign-bp-¶{X efn-X-ambn Ah-X-cn-¸n-¡p-hm-\mWv ChnsS {iaw.
3. N{a-h«w –þ imkv{X-tem-I-¯n\v tIc-f-¯n-semcp ]qWy-
`qan ]T-\-¯nsâ AYhm ]pXnb Is−-¯-ep-I-fpsS KXnsb amän \nÀ¯n, tIcfob kaq-l-¯n\v Gähpw A`n-am-\-I-c-amb hkvXpX Xs¶ BZyw ]d-bp-I-bmWv. Bcy-`-Sobw \ÂIp¶ sXfn-hp-I-f-\p-k-cn¨v (Cu ]T-\-¯nsâ c−mw-`m-K¯nse tPymXnx-im-kv{X-]-c-amb NÀ¨bpsS \nK-a-\§Ä) Bcy-`-Ssâ PohnXw sIm−v [\y-amb \½psS ]pWy-`qanbpsS A£mwiw Dw tcJmiw Dw BIp¶p. s]m¶m-\n-¡-Sp¯v, `c-X-¸p-g-bpsS Ic-bn imkvXmhnsâ km¶n²yw sIm−v [\y-amb N{a-h-«w. Cu N{a-h«w `mkvI-cm-Nm-cyÀ þH¶m-a³ ]d-bp¶ Aiva-I-P-\-]-Z-¯nsâ `mK-am-bn-cp-¶p.
Bcy-`-Ssâ tZiw kw_Ôn¨ hnhm-Zhpw ]pXnb sXfn-hp-Ifpw þ Ipkp-a-]p-chpw N{a-h-«hpw F§s\ icn-bmIpw? Bcy-`-Ssâ Øew GXmWv? Bcy-`-Ssâ e`y-amb IrXn-bnÂ, KoX-§-fn e`yamb Htc Hcp Øe-\maw Ipkp-a-]p-c-am-Wv. Bcy-`-S-\m ]cm-aÀin-¡-s¸-Sp¶ Ipkp-a-]pcw KwK-bpsS Xoc¯v (C-¶s¯ ]mä-\, ]gb ]mS-eo-]p-{X-¯n\v kao-]w) ssP\-kw-kvIr-Xn-bpsS tI{µ-am-bn-cp¶ \K-cn-bm-Wv. ssP\-XoÀ°-¦-c-
5
\mb alm-ho-c\pambn _Ô-s¸« Cu Øe¯v N{µ-Kp-]vX-au-cysâ amXm-a-l\mb DZ-b-`-{Z-\mWv Cu \Kchpw ChnsS hniz-{]-kn-²-amb \f-µ-sb¶ hnizhn-Zym-e-bhpw Øm]n-¨-sX¶v Icp-X-s¸-Sp-¶p. al-ho-c-\pÄs¸sS ]e ssP\-kn²-·mcpw KWn-X-¯n \njvWm-Xcpw kqcy-{]-Ú-]vXn, Pw_p-Zzo-]-{]-Ú]vXn apX-emb KWn-X-Ir-Xn-IÄ ssP\-]m-c-¼-cy-¯n e`y-am-Ip-Ibpw sNbvXp. D¯c-`m-c-X-¯nse Cu Úm\ImWvUw `{Z-_m-lp-hn-s\m¸w {imh-W-_ÂtKm-fbnepw (ssa-kqÀ, {In.-ap. 300) XpSÀ¶v tIc-f-¯n-ep-sa-¯n-b-t¸mÄ Ipkp-a-]pcw tIc-f-¯nepw {]Jym-X-am-bn. Cu ssP\-]m-c-¼-cyw D¯-c-tI-c-f-¯n C¶pw Zriy-am-Wv. Ipkp-a-]p-c-¯nsâ Cu ]Ým-¯-e-¯n \n¶p thWw \mw Bcy-`Ssâ _Ô-s¸« ]cm-aÀis¯bpw At±-l-¯nsâ tIc-f-hp-am-bp-Å-Xmbn sFXn-ly-§Ä ]d-bp¶ s]m¡nÄsImSn _Ô-s¯bpw hymJym-\n-t¡-−-Xv. Bcy-`-Sobw, KWn-X-]m-Z-¯nse BZy-tÇm-I-¯n-emWv Ipkp-a-]pcw ]cm-aÀin-¡s¸-Sp-¶-Xv. {_Ò-Ip-i-in-_p-[-`r-Kp-c-hn-Ip-P-Kp-cp-tIm-W-`-K-Wm³ \a-kvIrXy Bcy-`-S-kvXznl \nK-ZXn Ipkp-a-]p-tc-`yÀ¨nXw Úm\w {_Òw, `qan, N{µ³, _p[³, ip{I³, chn, IpP³, Kpcp, i\n, Xmcm-K-W-§Ä Chsb hµn¨v Bcy-`-S-\n-hnsS Ipkp-a-]p-c-¯n hmgv¯s - ¸-Sp¶ Adn-hns\ sNmÃp-¶p. Bcy`Sob-¯n\v Hcp \qäm-−n\v tijw `mkvI-cobw cNn¨ `mkvI-cm-Nm-cyÀ H¶ma³ (CE 629) Cu tÇmI-¯nsâ hymJym-\-¯nÂ, Ipkp-a-]pcw ]mS-eo-]p{X-am-sW¶v hyà-ambn ]d-bp-¶p. Ipkp-a-]p-tc-`yÀ¨nXw Úm\w `mkvI-csâ A`n-{]m-b-¯n Bcy-`-So-b-¯n\v ImX-emb kzmbw-`ph AYhm {_Ò-kn-²m´-am-Wv. tKmf-]mZw 49þ50 tÇmI-§-fn-embn Bcy-`-S³ ]d-bp-¶Xv {i²n-¨m \ap¡v Cu hkvXpX `wKn-bmbn a\-Ên-em-¡mw. kZ-k-Úm-\-k-ap-{ZmXv kap-²rXw {_ÒWx {]km-tZ\ kÚmt\m¯-a-cXv\w abm \naáw kza-Xn-\mhm {_Ò-tZ-hsâ {]km-Z-¯m {]m]-©n-I-amb Úm\-¯nsâ Cu D¯-a-cXv\w _p²n-bm-Ip¶ tXmWn-bm krjvShpw Akr-jvS-hp-amb ØnXn-I-fpsS Adnhnsâ kap-{Z-¯n \n¶pw F¶m D²-cn-¡-s¸-«p. Bcy-`-Sobw \mav\m ]qÀÆw kzmbw-`phw kZm kXyw kpIr-Xm-bptjmx {]Wmiw IpcptX {]Xn-I-©pIw tbmƒky Cu Bcy`So-bw, ]qÀÆ-ambn \ne-\n¶, \mi-an-Ãm¯ kzmbw-`p-h-kn-²m´w Xs¶-bm-Wv. kXy-amb Cu IrXnsb A\p-I-cn-¡p-¶-hcpsSbpw hnaÀin-¡p-¶hcpsSbpw BbpÊpw kpIr-Xhpw \in-¡p-¶p. ssP\-XoÀ°-¦-c-·m-cn Ej-`s\ AYhm BZn-\m-Y-s\ krjvSn-IÀ¯m-hmb kzbw-`q-hmb {_Òsâ Ah-Xm-c-ambn ssP\À ]cn-K-Wn-¡p-¶p. kXvþA-kXv AXm-bXv krjvShpw AkrjvShpamb Úm\-k-ap-{Z-¯n kzbw`qhm-Ip¶ {_Ò-tZ-hsâ Ah-Xm-c-amWv BZn-XoÀ°-¦-c³. BZn-bn Úm\w, Adnhv
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am{X-am-Wp-−m-bn-cp-¶-Xv. Adn-hn \n¶mWv kzbw-`q-hmb BZn-\m-Y\pw {]]©hpw D−m-Ip-¶-Xv. A§s\ ssP\-cpsS Úm\-tZ-h-\mb {_Ò-s\bmWv Bcy-`-S³ Xsâ IrXn-bpsS BZy-tÇm-I-¯nepw hµn-¡p-¶-Xv. {]Wn-]-ssXy-I-a-t\Iw Iw kXymw tZhXmw ]cw {_Ò Bcy-`-S-kv{XoWn KZXn KWnXw Ime-{Inbmw tKmfw
( 1)
]c-a-k-Xy-amb{_ÒtZhs\, H¶pw A\-h-[n-bp-amb {_Òs¯ {]W-an¨v Bcy`-S³ {Xnhn-[-am-bn-cn-¡p¶ KWn-Xw, Ime-{In-b, tKmfw Chsb ]d-bp-¶p. Ipkp-a-]p-c-hp-ambn Bcy-`-Ss\ _Ô-s¸-Sp-¯p¶ FÃm sFXn-ly-§Ä¡pw sFXn-lym-Sn-Øm-\-¯n Na-¡-s¸« tÇmI-§Ä¡pw ASnØm\w At±-l¯nsâ apI-fn ]dª ]cm-aÀi-am-Wv. Úm\-hn-Úm-\-§-fpsS hnf-\n-e-amb Ipkp-a-]p-c-¯n hmgv¯-s¸« kn²m´w F¶p-am-{Xta Cu ]cm-aÀi-¯n\v AÀ°-ap-Åp. ]n¡m-e¯v Cu hkvXpX ad¶v Bcy-`-Ss\ Ipkp-a-]p-c-\n-hmkn-bm-¡p¶ hn[¯n tÇmI-§Ä Na-¡-s¸-«p þ kqcyx kzbw Ipkp-a-]p-cy-`-hXv Ieu Xp `qtKm-f-hnZv Ipe]x Bcy-`-Sm-`n-[m\x6 Ien-Im-e-¯n kqcy³ kzbw Ipkp-a-]p-cn-bn `qtKm-f-hn-Zzm-\mbpw Ipe-]-Xnbmbpw Bcy-`-S-s\¶ t]tcmsS Ah-Xc - n¨p. Bcy-`-Ssâ IrXn-IÄ¡v, {][m-\-ambpw Bcy-`-So-b-¯n-\v, `mcX¯nepw Ad-_nI-fpsS CS-bnepw kn²n¨ {]Nm-c-s¯-¸än Ncn-{X-Im-c-·m-scÃmw GIm-`n-{]m-b¡m-cm-Wv. `mjy-Im-c-·m-cn s]« Bcy-`-S-in-jy-\mb {]`m-I-cs\¸än aäp ]WvUn-X-·m-cpsS ]cm-aÀiw am{Xta e`y-am-bn-«p-Åp. {InkvXp-hÀjw 629  ]ÝnaKpP-dm-¯nse hÃ-`n-bn (ku-cm-jv{Sw) Pohn-¨n-cp¶ `mkvI-cm-Nm-cyÀ H¶m-a³ Bcy-`-S-in-jy-]-c-¼-c-bnse Gähpw {]kn-²-\mb hymJym-Im-c-\m-Wv. Xsâ Bcy-`-So-b-`m-jy-¯n\v7 ]pd-sa, alm-`m-kvI-cobw, eLp-`m-kvI-cobw8 F¶n-§s\ Adn-b-s¸« At±-l-¯nsâ IÀ½-\n-_Ôw Bcy-`-So-b¯ - n\v Gähpw {]mam-Wn-I-amb `mjyw \ÂIn. Z£n-W-Kp-P-dm-¯nse `nÃ-a-e-bn Pohn-¨n-cp¶ {_Ò-Kp-]vX³ {InkvXp-hÀjw 628  hnaÀi-\-¯nsâ sImSp-¦mäv Agn-¨p-hn-«p-sh-¦nepw ]n¡m-e¯v BcymÀ²-cm-{X-kn-²m´w Bkv]-Z-am¡n JWvU-Jm-Zy-I-sa¶ Ic-W-{KÙw cNn¨v Bcy-`-Ssâ JymXn¡p ap¼n ASn-b6
Dr. Kern 1874  (Leden, Holland) {]kn-²o-I-cn¨ Bcy-`-So-b-¯nsâ BwK-e-]cn-`m-j-bn D²r-X-amb Cu tÇmI-¯nsâ Dd-hnSw hyà-a-söv i¦À _meIrjvW Zo£nXv `mc-Xob tPymXnx-imkv{X Ncn{X¯n ]d-bp-¶p. `mKw: II ]pdw 60. 7 Bcy-`-Sobw þ`m-kvIc (I), tkmta-izc `mjy-§-tfm-sS, ]cn-tim-[-I³: Ir]m-i¦À ip¢, C´y³ \mj-W kb³kv A¡m-Z-an, \yqsUÂln. (1976). 8 alm-`m-kvI-co-bhpw eLp-`m-kvI-co-bhpw Ir]m-i-¦Àip-¢-bpsS ]cn-tim-[-\tbmSpw Bap-J-t¯mSpw eI\u kÀÆ-I-em-ime {]kn-²o-I-cn-¨n-«p-−v.
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dhv ]d-ªp. tkmta-iz-csâ hymJym\w e`y-sa-¦nepw At±-l-¯nsâ Imew Xn«-a-Ã. ]Xn-s\m¶mw \qäm-−mImw F¶ A`yqlw ip¢-bpsS Bcy-`-So-b¯nsâ BwK-e-]-cn-`m-j-bn \ÂIn-bn-cn-¡p-¶p. ]Xn-aq¶mw \qäm-−n tNmfcm-P-[m-\nsb (Kw-Km-]pcn AYhm KwssK-sIm-−-tNm-f-]p-cw) Ae-¦-cn-¨n-cp¶ kqcy-tZ-htkma-kp-X\mWv (b-Pzm³, -Zo-£n-XÀ F¶pw t]cv tcJs¸-Sp¯n-¡mWp-¶p) (P-\\w: {InkvXp-hÀjw 1192) asämcp {]kn² hymJym-Xm-hv. Bcy-`-Ss\-¸än Øe-Im-e-kw-_-Ôn-bmbn Imcy-amb hnh-c-§-sfm¶pw kqcy-tZ-h³ \ÂIp-¶n-Ã. Bcy-`-S³ \ÂIp¶ ssP\-þ-bp-K-LS\bpsS hymJym\w X\n¡p hyà-a-söv ]d-bp¶ kqcy-tZ-h³ tKmfw, tÇmIw 14 sâ hymJym-\-¯n DÖ-bn-\n-bpsS tcJmwiw 24 Un{Kn-bm-sW¶v hcpw hn[w tÇmI-¯n ]©-Zimwti F¶v amäw hcp-¯p-¶p. kqcy-tZ-h-\p-tijw tIc-fo-b-cmb ]c-ta-iz-c\pw (AD1450) \oe-I-WvT-tkm-a-bmPnbpw (AD1500) Bcy-`-So-b-¯n\v hymJym-\-§Ä cNn-¨p-sh-¦nepw, BÀ¡pw Xs¶ Bcy-`-S-s\-¸än `mkvI-c³þI ]d-bp-¶-Xn Ihnªv bmsXmcp hnh-chpw e`y-am-bn-cp-¶n-Ã. `qXn-hnjvWp (Im-©o-]p-cw), cLp-\m-Y-cm-P³, bÿ C§s\ Bcy-`-So-b-¯n\v hni-I-e\w \ÂInb hnZzm-·mcpw `mkvI-co-bw, Ic-W-c-Xv\w, {Kl-Nm-c-\n-_-Ô-\w, injy-[o-hr-²nZw, Ic-W-{]-Im-iw, `S-Xpeyw C§s\ \nch[n IrXn-I-fn-eqsS Bcy`Ss\ Imem-\p-kr-X-ambn ]n´pScp-¶p-hcpap−mbn«pw Bcy-`-Ssâ kztZiw Fhn-sS-bm-sW-¶Xv XÀ¡-hn-j-b-am-Wv. HutZym-KnI-þ-K-th-j-W-¯nsâ Np¡m³ ]nSn-¡p-¶-hÀ Aiva-Iw, Ipkp-a-]pcw apX-embn `mkvI-c³þI ]d-bp-¶ hnh-c-§sf B{i-bn¨v Bcy-`-S³ tKmZm-h-cn-bpsS sX¡³I-c-bn Aiva-I-sa¶ P\-]-Z-¯n ]nd¶v Ipkp-a-]p-c¯v Ipe-]-Xnbmbn Pohn¨bmfm-Wv. kucm-jv{Shpw A]-cm-´-Ihpw sIm¦-Whpw t]mse ssP\-þ-_u-²-tc-J-I-fnse Aiva-Iw {]mNo\ P\-]Zambn-cp-s¶-¦n C¶v \ne\n¡p¶ Ahy-à-X¡v Hcp Imc-W-hp-an-Ã. ssP\-þ-_u² ]menenJn-X-§sf B{i-bn¨v AivaIw tKmZm-h-cn-bpsS sX¡³Ic-sb¶v ]d-bp-¶-hÀ Bdmw \qäm-−n C§s\-sbmcp cmPyw \ne-\n-¶-Xmbn hyà-ambn ]d-bp-¶n-Ã. `mkvI-c³þI ]d-bp-¶ AivaIw GXv Øe-amWv? Bcy-`-Ssâ Øew kw_Ôn¨ hnhm-Z-§Ä¡-Sn-Øm\w Xs¶ AivaIw kw_-Ôn¨ Ahy-à-X-bm-Wv.
Ncn-{X-Im-c-·m-cpsS ZrjvSn-bn Bcy-`-Ssâ kztZ-i-s¯-¸än Ncn-{X-Im-c-·mÀ \ÂIp¶ {][m\ hnh-c-W-§Ä Xmsg \ÂIp-¶p. i¦c_me-Ir-jvW-Zo-£nXv (`m-c-Xob tPymXnx-imkv{Xw, `mKwþII) Bcy-`Sobw Bkv]-Z-amb Ime-K-WnXw alm-cm-jv{S-bnepw hmcm-W-kn-bnepw iI 1400 \v tijw \ne-hn-hn-Ã. Bcy-kn-²m´w \ne-\n¡p-¶Xv Z£n-W-`m-cX-¯nepw {]tXy-In¨v ae-_mÀ tZi-¯p-am-Wv. Xan-gv-þ-ae - -bm-f-tZ-i-§-fnse kucþ-]-©mw-K-W\ Bcy-`S ]mc-¼-cy-¯n-e-[n-jvT-am-Wv. Dr. Kern {]kn²oI-cn¨ Bcy-`-Sobw aq¶v ae-bm-f-¯n-epÅ ssIs¿-gp-¯v{]-Xn-IsfbmWv Ahw-e-_n-¨Xv. IÀ®m-S-I-¯n-sebpw ssakq-dn-sebpw henb P\-hn-`m-K-amb sshjvW-hÀ Bcy-]£w ]n´p-S-cp-¶-h-cm-sW¶pw {io. Zo£nXv ]d-bp-¶p. Bcy-kn-²m´w
8
]mäv\sb (Ip-kp-a-]p-cw) DÄs¡m-Åp¶ _wKmÄ tZi¯v {]kn-²-a-sö hkvXp-Xbpw Ipkp-a-]pcw Z£n-W-tZ-i-¯pÅ GtXm Øe-am-bn-cn-¡m³ km²y-X-bp-s−¶pw, XoÀ¸v IÂ]n-¡m-\m-In-söpw At±lw hyà-am-¡p-¶p.
s{]m^. Ir]m-i-¦Àip-¢, tUm.-sI.-hn. iÀ½ C´y³ \mj-W kb³kv A¡m-Zan {]kn-²o-I-cn¨ Bcy-`-So-b¯ - nsâ BwK-e-]-cn-`m-j-bn 'kwi-b-¯nsâ Omb H«pw Xs¶ CÃmsX Bcy-`-S³ Ipkp-a-]p-c¯v (C-¶s¯ ]mäv\) Pohn-¨n-cp-¶-Xmbn' hyà-am-¡-s¸-Sp-¶p. Bcy-`-S-s\-¸-än-bpÅ Kth-j-W-¯n `mkvI-c³ H¶m-asâ Biva-Iobw F¶v Bcy-`-So-b-¯n\v e`y-amb hntijWw Imcy-amb NÀ¨¡v hnj-b-am-bn-«p-−v. Ir]m-i-¦À ip¢-bpsS `mkvI-c-þ-tkm-ta-iz-c-`m-jy-§-fpsS {]kn-²o-I-c-W-¯nÂ9 _u²-cpsS ]menenJn-X-§sf D²-cn¨v alm-P-\-]-Z-am-bn-cp¶ Aiva-Iw tKmZmh-cn¡pw \À½-Z¡pw CS-bn (tKm-Zm-h-cn¡pw amln-jva-Xn¡pw CS-bnÂ) ØnXn sNbvXn-cp-¶p-sh¶v ]d-bp-¶p. Hudw-K-_m-Zn\v sX¡v Ing-¡mWv AivaI-¯nsâ Xe-Øm-\-amb {]Xn-jvTm\w AYhm ssP\-cpsS s]mb-W-]pcw F¶pw ip¢ ]d-bp-¶p. D¯-c-þ-]-Ýn-ta-´y-bnepw Hcp AivaIw \ne-\n-¶-Xmbn hcm-l-an-ln-c-s\bpw {Ko¡v tcJ-I-sfbpw D²-cn¨v ]ecpw kn²m-´n-¡p-¶p. hÃ`n-bn Xma-kn-¨n-cp¶ `mkvI-c³ H¶m-a³ ]d-bp¶ AivaIw C{µ-]p-cn-bmb C³tUm-dn\v sX¡p-−m-bn-cp¶ Aiva-I-am-sW¶v ip¢ Xd-¸n¨v ]d-bp-¶p.
4. AivaIw FhnsS? Imcy-amb sshI-ey-§-fpÅ \nK-a-\-§-fmWv ChnsS e`y-am-Ip¶ Kth-jW ]Ým-¯-ew. Xmsg ]d-bp¶ Imcy-§Ä {i²n-¨m IqSp-X imkv{Xo-bhpw hniz-k-\o-b-hp-amb \nK-a-\-¯n-se-¯pI km²y-am-Wv. Bcy`Ssâ {]kn-²-amb {]mtW-ss\Xn Iemw`qx F¶ hmIy¯nse `qxhns\ `w B¡n `qan-bà \£-{X-N-{I-amWv Id-§p-¶Xv F¶v kn²m´n¨ `mkvI-c³ Bcy-`-Ssâ t\Àin-jy-\-Ã. Bcy-`-S\v Hcp \qäm-−n\v tijw Pohn¨ ssih-\mWv hÃ-`n-bn \mw ImWp¶ `mkvI-c³. `mkvIc³ hnti-jn-¸n-¡p¶ Xc-¯n-epÅ Biva-Iob tPymXnÀK-WnXw þ Hcp KWn-X-]m-c-¼cyw þ \ne-\n¶ Htcsbmcp Øew tIc-f-am-Wv. alm-cm-jv{Sbn-tem, amln-jva-Xn-bntem Hcp kn²m-´-tam, BNm-cy-t\m, injy-]-c-¼ctbm sFXn-ly-§Ä t]mep-an-Ã. 2. tIc-fo-b-amb Bcy-`-So-b-¯n\v Biva-Iobw F¶v `mkvI-c³ F´p-sIm−v hntijWw \ÂIn? (a) `mkvI-cm-Nm-cyÀþI, No\-k-©m-cn-bmb lpbm³kmwKnsâ bm{Xm-Im-e¯v (AD 630þ644) kucm-jv{S-bnse cmPm-hm-bn-cp¶ _u²-\mb {[ph-`-«sâ B{in-X-\m-bn-cp-¶n-cn-¡msa¶v Icp-X-s¸-Sp-¶p. 1.
9
Āryabhatīya with the commentary of Bhāskara-I and Someśvara, p. xxv, Indian National Science Academy (1976), New Delhi-2.
9
(b) ssih-\mb
`mkvI-c³, tIc-f-¯n ssP\-]m-c-¼-cy-¯n DÛ-hn¨ tPymXnÀK-Wn-X-¯n\v Aiva-Iobw F¶v t]À hnfn-¡m-\n-S-bpt−m? (c) ssP\-cpsS AivaIw Fhn-sS-bmWv? aucy-Imew apX \ne-\n¡p¶ {ih-W-_ÂtKm-f-bn-sebpw [À½-Ø-e-bn-sebpw ssP\þP\-]-Z-§Ä, Aiva-Io-b-\mbncp¶ _mlp-_-en-bpsS cmPy-¯nsâ `mK-am-bn-cp-¶ntÃ? {ih-W-_ÂtKm-f-bpsS A£mwiw 12N51Dw tcJmwiw 76E29 Dw BIp-¶p. [À½-Ø-e-bp-tSXv A£mwiw 12N53Dw tcJmwiw 75E23 Dw BIp-¶p. Cu kml-N-cy-¯nÂ, c−v Un{Kn am{Xw sX¡mb (10N51Dw75E45) N{a-h«-¯-¸sâ Øm\-amb N{a-h«w ssP\-cpsS ]pWy-`q-an-bmb Aiva-I-¯nsâ `mK-am-bn-cp¶p F¶v Icp-Xp-¶-Xn sXäpt−m? (d) ssP\-cpsS sFXn-ly-a-\p-k-cn¨v Ej-`-tZ-hsâ tPyjvT-]p-{X-\mb `c-X³ Atbm²y Xe-Øm-\-am¡n D¯-c-`m-c-Xhpw Cf-b-a-I³ _mlp-_en (Aiva-I³?) s]mb-W-]pcw BØm-\-ambn Z£n-W-tZ-ihpw, AXm-bXv AivaIhpw `cn-¨n-cp-¶p. D¯-c-tZiw AXn-\m `mc-Xhpw Z£n-W-tZiw Aiva-Ihp-am-bn-¯oÀ¶p. `c-X\pw _mlp-_-en-bp-ap-−mb Alnw-km-]-c-amb ZrjvSnbp²w, Pe-bp-²w, aÃ-bp²w Ch-bn `c-X³ ]cm-P-bs - ¸-«p-sh-¦nepw alm-tbm-Kn-bmb _mlp-_-en AYhm Aiva-I³ Zo\m-\p-I-¼-bmepw `cXsâ tamlm-th-i-¯nepw ¢n¶-\mbn Xsâ cmPyw `c-X\v hn«p-sImSp¡p¶ IY ssP\-]p-cm-W-¯n ]d-bp-¶p.10 (e) Cu sFXn-ly-¯nsâ ]Ým-¯-e-¯nÂ, N{µ-Kp-]vX-au-cy-t\m-sSm¸w `{Z_m-lp-hnsâ Z£n-W-tZ-i-t¯-¡pÅ {In.-ap. aq¶q-dm-am-−nse ]em-b\w _mlp-_-en-bpsS Aiva-I-¯n-te-¡m-bn-cp-¶p-sh¶v \ap¡v a\-Ên-em-¡mw. (f) _mlp-_-en-bpsS
Øm\-Xym-K-t¯m-sS-bmWv D¯-c-þ-Z-£n-W-am-bn-cp¶ Atbm-²ybpw Aiva-Ihpw `c-X-N-{I-hÀ¯n-bpsS Iogn `mc-XhÀj-am-bn¯oÀ¶-Xv. Cu hkvXp-X Bcy-`-So-b-¯n bpKm-cw-`-IÂ]-\-bn kqNn-Xam-Wv. KoXnI 5 þ
10
http://www.jainworld.com/book/the_sacred_sravana_belagola/ch8.asp: The follow- ing legend is given at this site: Bahubali, the first Jaina saint to attain liberation in this ‘ avasarpin kala’, i.e., the descending half arc of time , was the son of Lord Rshabha, the first Jaina Tirthankara, who flour-ished at the dawn of civilization and taught mankind the first lessons of a cultured life. Lord Rshabha-deva, the son of Nabhiraja and Marudevi, was a patriarch king of Ayodhya. Lord Rshabha-natha had many sons.among whom Bharata and Bahubali were very prominent.Bharata was the crown-prince and he succeeded his father to the throne of Ayodhya. By his prowess Bharata became the first universal monarch and due to his profound impact on the country, India came to be known as '' Bharatavarsha'', i.e., the land of Bharata. Bahu-bali was given the kingdom of ‘ Asmaka’ form south India which he ruled from its capital seat at podanapura. In this way after dividing his kingdom among his sons, Lord Rshabha- deva retired to the Himalayas and adopted the Jaina ascetic way of life to teach mankind the path of salvation.
10
Imtlm- a-\thm V a\p-bpKmx ivJK-XmkvtX N a\p-bpKmx Oq\m N IÂ]m-tZÀbp-K-]mZm K N Kpcp-Zn-h-km¨ `c-XmXv ]qÀÆw ( 5) Cu KoX-¯nsâ Ah-km\ `mKw `mc-XmXv ]qÀÆw F¶mWv ]mc-¼-cy-kn-²-ambn-cn-¡p-¶-Xv. CXv icn-b-Ã. `mc-X-bp-²-¯nt\m, `mc-X-bp-²-¯n\v ap¼mbn IenbpKw XpS-§n-sb¶ A_-²-[m-c-Wt¡m Bcy-`-S\v apt¼m, ]g-b-Im-et¯m bmsXmcp [mc-Wbpw D−m-bn-cp-¶n-Ã. alm-`m-cXw A\p-k-cn¨v Ipcp-t£-{X-bp²-¯n\v 36 hÀj-§Ä Ign-ªmWv {ioIr-jvWsâ \n[-\hpw Ien-bp-Km-cw-`hpw. B ØnXn¡v `mc-XmXv ]qÀÆw Ien-bp-Km-Zn¡v aps¼¶v hymJym-\n-¡-s¸Sp-¶Xv F{XI−p icn-bmWv? Cu KoX-¯nse ]cm-aÀiw ssP\-bp-K-k-¦Â]hpw sFXn-ly-hp-am-Wv. `c-XmXv ]qÀÆw F¶Xv bpKm-Zn- Ej-`-\m-Ysâ ]p{X-\mb `c-Xsâ ImeL«-am-sW¶ ssP\-hn-izm-k-¯nsâ {]Xn-^-e-\-am-Wv. km{¼-Zm-bn-I-ambn \ne-\n¶ {_mÒW-cpsS 4:3:2:1 ssZÀLy-amÀ¶ IrXm-ZnbpK-L-S-\sb Bcy-`-S³ ka-Xp-ey-amb NXpÀbp-K-am¡n amän-a-dn-¨Xpw ssP\-kzm-[o-\-¯m-em-Wv. tIc-fob {_mÒ-W]m-c-¼-cy-tc-J-I-fn Bcy-`-Ss\ ]cm-aÀin-¡m-¯-Xn\p Imc-Whpw Bcy-`-Ssâ ssP\-_-Ô-am-Wv. `c-X-t\mSp IqSn A]-kÀ¸n-Wn-bmb Ien-bp-Km-cw`w BWv Bcy-`-S³ kqNn-¸n¡p-¶-sX¶ hkvXpX Ime-{In-b, tÇmIw 9  \n¶pw a\-Ên-em-¡mw. DÕÀ¸nWo bpKmÀ²w ]Ým-Z-]-kÀ¸nWo bpKmÀ²w N at[y bpKky kpj-amƒƒZmht´ Zpj-ta-µq-¨mXv (Ime{Inb: 9) Hcp alm-bp-K-¯nsâ BZy-]-IpXn DÕÀ¸n-Wnbpw c−mw `mKw A]-kÀ¸n-Wnbp-am-Wv. kpjam a²y-¯nepw Zpjam Bcw-`m-h-km-\-§-fn-ep-am-Ip-¶p. KXImew N{µ-Xpw-Ks\ B{i-bn¨v \nÀ®-bn-t¡-−-Xm-Wv. ssP\-cpsS Cu bpK-K-W-\-bn alm-bp-K-¯nsâ ]{´−v hn`m-K-§-fn BZy aq¶pw Ah-km\ aq¶pw hn`m-K-§Ä Zpj-abpw a[y-§-fmb Bdp-hn-`m-K-§Ä kpj-abpamWv. 360,000x 12 = 432,000,0. Ch-bn 360000x 3 = 108, 000,0 Ien-bp-K-am-Wv. Cu
Ien-bpKw Ah-km\ aq¶v hn`m-Ks¯ DÄs¡m-Åp-¶-Xn-\m A]-kÀ¸n-WnbpsS Ah-km-\-amb Zpj-a-bm-Wv. 360000 hÀj-§-fn 131493125 Znh-k-§fpw Ch-bn IpP-Kp-cp-ip-{I-·mÀ¡v
]qÀ®-{`-a-W-kw-Jy-Ifpw kqcy³, N{µ³ apX-emb N{µ-Xpw-K-sam-gn-¨pÅ a[y-a§Ä¡v kq£va-bp-K-§-fp-−v. N{µ-Xp-K-¯n\v Cuhn-[-amb bpKJ-WvU-§-fn-Ãm¯-Xn-\-emWv DÕÀ¸n-Wym-Zn-bmb JWvU-\nÀ®-b-¯n\v N{µ-Xpw-Ks\ Bcy-`S³ \nÀt±-in-¡p-¶-X.v 11 11
Abraded Yugas of Mean Longitudes are given at p.93, KS Shukla, Āryabhatī yam, INSA, New Delhi-2
11
bpK- A]-kÀ¸n-Wn-þ-Zp-j-am-cw-`-amb ssP\-cpsS 360000x 3 = 108, 000,0 Ien-bpKsa¶, Zpj-amþalm-bp-K-JWvUw XpS-§p-¶Xn\v alm-`m-c-X-bp-²-hp-ambn F§s\ _Ôw IÂ]n¡mw? Ej-`-\m-Ysâ aI-\mb `c-X\pw _mlp-_-en-bpam-bpÅ bp²-¯n\p tijw _mlp-_en cmPy-XymKw sNbvXv `c-X³ N{IhÀ¯n-bm-Ip-¶-XmWv ssP\-cpsS bpKm-Zn. `cXmXv ]qÀÆw F¶ Bcy-`-Ssâ bpKmZn \nÀÆ-N-\-¯n\v ImcWw ChnsS hyà-am-Ip-¶p. (g)
IS-en t]mbn {KlWw I−-Xn\v {`jvSv IÂ]n-¡-s¸« Bcy-`-S³ {_mÒ-W-hn-izmkw Dt]-£n¨v ssP\-aXw kzoI-cn-¡p-Ibpw A§s\ ssP\-k-¼À¡-¯m Ipkp-a-]p-c¯p t]mIp-Ibpw Ahn-sS-bp-−m-bn-cp¶ ssP\-hn-Zym-]o-T-¯nsâ Ipe-]-Xn-bm-Ip-Ibpw sNbvXp F¶-XmIWw icnbmb hkvXp-X.
`mkvI-c-s\m-¶m-a\v ka-Im-en-I-\m-bn-cp¶ ]pen-tIin c−m-a³ Pbn¨ \nc-h[n cmPy-§-fpsS ]«n-I-bn (\f, aucy, IZw-_-Ip-e-§Ä, Ime-Nq-cn, tch-Xn, h\hm-kn, KwK, Aep-], sIm¦-Ww, ]pcn, emSw, amf-hw, KpÀP-cw, IenwKw, tImkew, alm-cm-jv{S-Iw, ]njvS-]p-cw, ]Ã-h-Im-©o-]p-cw. tNmf, ]mWvUy-tI-cfw C§s\ kÀÆ-cm-Py-§-sfbpw enJn-X-¯n ]cm-aÀin-¡p¶p) Aiva-I-sa¶ alm-cm-jv{S-bnse tZiw DÄs¸-Sp-¶n-sÃ-¶Xv {i²n-t¡− kwK-Xn-bm-Wv. `mkvI-c³ ]d-bp¶ AivaIw A¡m-es¯ cmjv{So-b-`q-]Sw Bkv]-Z-am-¡n-bsöv sFtlmÄ enJn-X-¯n \n¶pw a\-Ên-em-¡mw. ip¢-bp-sSbpw aäv tKmZm-hcnþA-iva-I-hm-Zn-I-fp-sSbpw \nK-a-\-§Ä ASn-Øm\cln-X-am-sW¶v ChnsS sXfn-bp-¶p.
5. `c-XmXv ]qÀÆw `mc-X-bp-²-am-¡nb Ime-K-W\ Ien-bp-Km-Zn-bpsS apI-fn ]dª `c-X-Im-e-L«w Bkv]-Za - mbn ]n¡m-e¯v Ien-bp-KmZn kwh-Õ-c-K-W\ D−m-bn. Cu kwh-Õ-c-K-W-\¡v Z£n-W-`m-c-X¯n ssP\-k-¼À¡-ap-−m-bn-cp¶ IÀ®m-S-I-¯nemWv BZyw {]Nmcw kn²n¨-sX¶v Nmeq-Iy-cm-Pm-hmb ]pen-tI-in-bpsS sFtlmÄ inem-en-Jn-X-¯n 12 \n¶pw a\-Ên-em-¡mw. Ien-h-Õcw \ÂIp¶ BZy inem-en-Jn-X-am-Wn-Xv. `cXmXv F¶ chn-IoÀ¯n-bpsS {]tbmKw Bcy-`-Sobw B{i-bn-¨m-sW¶v IenhÀjw \ÂIp-¶-Xn \n¶pw a\-Ên-em-¡mw. Ien-h-Õcw BZy-ambn \ÂIp¶ Cu (AD 634) enJnXw Bcw-`n-¡p-¶Xv Pnt\{µs\ kvXpXn-¨p-sIm-−m-Wv. Ien-bp-K-h-Õ-c-K-W\ ssP\-]m-c-¼-cy-¯neqsS {]kn-²-amb kwK-Xn-bpsS kqN\ ChnsS e`n-¡p-¶p. sFtlmÄ Bcy]p-c-am-sW¶ sFXnlyw ssP\-kn-²-\mbn¯oÀ¶ Bcy-`-Ssâ t]cn ssP\À Øm]n-¨-XmImw Cu \K-cn-bpsS BZn-cq]w F¶ Dulm-t]m-l¯n\pw kwK-Xn-bp-−v.
12
Text of the inscription is available at the site – http://projectsouthasia.sdstate.edu/docs/HISTORY/primarydocs/Epigraphy/AiholeInsc ription.htm
12
sFtlmÄ inem-en-Jn-X-¯nsâ hmb-\-bnepw hymJym-\-¯nepw KoXn-Im þ5 sâ hmb-\-bnepw hymJym-\-¯n-ep-ap-−mb kvJenXw kw`-hn-¨n-«p-s−¶v Xmsg \ÂIp¶ enJn-X-¯nse tÇmI-¯n \n¶pw a\-Ên-em-¡mw.13 {XnwiÕp {Xnk-l-t{kjp `c-XmXv Bl-hm-ZnXx k]vXm-_vZ-i-X-bp-tàjp itX-jz-_vtZjp ]©kp (33) ]©m-iÕp Ieu-Imte jSvkp-]-©-i-Xmkp N kamkp ka-Xo-Xmkp iIm-\m-a]n `q`pPmw (34) ChnsS BZy-h-cn-bnse `c-XmXv F¶ Bcy-`-Ssâ {]tbmKw Xs¶ chnIoÀ¯nsb¶ ssP\-Ihn enJn-X-¯n Bcy-`-So-b-¯nse ssP\-bp-K-K-W\ A\p-k-cn¨v D]-tbm-Kn-¨n-cn-¡p-¶p. 33-34 tÇmI-§-fpsS `mc-XmXv F¶ hmb\bpw B hmb-\sb `mc-X-bp-²-am-¡p¶ hymJym-\mhpw alm-`m-c-Xw, `mK-h-Xw, ]pcm-W-§Ä Ch-bnse `mc-X-bp-²-kw-_-Ôn-bmb ]cm-aÀi-§Ä¡v hncp-²-amWv. 1.
alm-`m-c-X-¯nse {]Jym-X-amb ]cm-aÀihpw KmÔm-co-im-]hpw A\p-kcn¨v Ipcp-t£-{X-bp-²-¯n\v tijw 36 hÀj-§Ä Ign-ªmWv IrjvW-\n-[\hpw Ien-bp-Km-cw-`-hpw.
2.
`mK-h-Xhpw {_Òm-WvU-]p-cm-Whpw A\p-k-cn¨pw Ipcp-t£-{X-bp²w Ignªv 36 hÀj-§Ä Ign-ªmWv IrjvWsâ \n[-\hpw Ien-bpsS BhnÀ`m-hhpw þ bkvan³ IrjvtWm Znhw bmXx Xkvan-t¶h XZm-l\n þ Ien-bp-Km-cw`w F¶ Imcy-¯n `mc-Xob kaq-l-¯n\v bmsXmcp kwi-b¯n\pw Imc-W-an-sÃ-¶n-cn-s¡, `mcXbp²s¯ Ien-bp-Km-Zn-bm-¡p¶ hymJym\w F§s\ icn-bmIpw?
3.
hcm-l-an-ln-cm-Nm-cyÀ k]vXÀjn-Nmcw \ÂIp-t¼mÄ Bk³ aLmkp ap\bx CXym-Zn-bmb tÇmI-¯n bp[n-jvT-csâ Imew Ien-hÀjw 653 AYhm iIm-cw-`-¯n\v 2526 hÀj-§Ä ap¼m-sW¶v ]d-ªn-cn-¡p-¶p. `mcXmXv F¶ hmb-\bpw `mc-X-bp-²-am-¡p¶ hymJym-\hpw AXn-\m hcml-an-ln-c\mepw \ncm-I-cn-¡s¸Sp¶p.
4.
alm-`m-c-X-¯n-sebpw ]pcm-W-§-fn-sebpw hkvXp-X-IÄ Xn«-ap-−m-bn-cp¶ ]c-ta-iz-cm-Nm-cyÀ Xsâ Bcy-`-Sob hymJym-\-¯n `mc-XmXv F¶
13
(33)When thirty (and) three thousand and five years besides, joined with seven hundred years, have passed since the Bhārata war; (3735 years = 634CE)
(34) And when fifty (and) six and five hundred years of the Saka kings also have gone by in the Kali age; (556 years of Saka Era = 556+78 = 634) (35)This stone mansion of Jinendra , a mansion of every kind of greatness, has been caused to be built by the wise Ravikirti, who has obtained the highest favour of that Satyashraya whose rule is bounded by the three oceans.
13
kvJen-Xs¯ ]mWvU-h-cpsS alm{]Øm\w F¶ Bi-b-t¯m-sS-bmWv hymJym-\n-¨n-cn-¡p-¶-Xv. 5.
`mc-XmXv F¶ KoXnI 5 sâ hmb-\bpw sFtlmÄ enJn-X-¯nsâ hmb\bpw sXäm-sW¶v CXn-\m sXfn-bp-¶p. – `mc-Xob Ime-K-W-\-bn \ne-\n¡p¶ `mc-X-bp-²-Imew, ]mWvU-h-cpsSbpw IrjvW-sâbpw Imew Ch kw_-Ôn¨ hnhm-Z-¯nse Bcy-`Sobm[njvThpw sFtlmÄ enJn-Xm-{inXhpamb 3102 BC hmZ-¯n\v imkv{Xo-bhpw Ncn-{X-]-c-hp-amb ASn-Øm-\-an-söv CXn-\m sXfn-bp-¶p. hnjvWp-]p-cm-W-a-\p-k-cn¨v þ alm-]-ßm-`n-tj-ImXv Xp bmh-Ö-·-]-co-£nXmx Ghw hÀj-k-l{kw Xp tÚbm ]©m-i-Zp-¯cw F¶v hnjvWp-]p-cm-W-¯n-epw `mK-h-X-¯n-epw e`y-amb ]cm-aÀi-§fpw cmP-hw-im-hen \ÂIp¶ ]co-£n¯nsâ Imehpw \ncm-I-cn¨v (alm-]ß\µ\v ap¼v 1015 hÀj-§Ä) 3102 BC ¡pÅ hmZw Ah-km-\n-¸n-¡m-sa¶v Bcy-`-So-b-¯nepw sFtlmÄ enJn-X-¯nepw {]Xy-£-s¸-Sp¶ `c-X³ hyà-am-¡p-¶p. `mc-Xo-b-Im-e-K-W\bnse {]kn-²-amb `mc-X-Im-e-L«w kw_-Ôn¨ 1400 BC þ3102 BC hnhmZw Bcy-`-So-b-¯nse `c-X³ Ah-km-\n-¸n-¡p-sa¶v
\ap¡v {]Xym-in-¡mw.
6. N{a-h-«-¯-¸-s\¶ imkvXmhv _mlp-_-entbm? cmPyw XyPn¨v tbmKn-bmbn amdnb alm-tbm-²-hmb _mlp-_e - n-bmWv imkvXm-sh¶ N{a-h-«-¯-¸³. \njvT-bp-sSbpw \nkzmÀ°-X-bp-sSbpw aqÀ¯nbmb tbmKo-iz-csâ, Ien-Ime ssP\-kn-²s\ ]n¡m-e¯v Na-¡-s¸« hymP ]qcm-W-§Ä IÅ-¡-Y-bn-eqsS sshjvW-h-aqÀ¯n-bm-¡n. IÀ®m-S-I-bnse AYhm Z£n-W-`m-c-X-¯nse ssP\-]m-c-¼cyw sshjvWh k{¼-Zm-b-¯n\v hgn-am-dn-bXv N{a-h-«-¯-¸sâ t]cpamä-¯n\v Imc-W-am-bn-¯oÀ¶p-sh¶v IcpXmw. ssP\-þ-_u-²-þ-ssh-jvWh k{¼-Zm-b-§-fpsS Hcp k¦-en-X-Nn-{X-amWv ]pcm-X\ tIcfw {]Xn-^-en-¸n-¡p-¶-sX¶ Ncn-{X-Im-c-·mcpsS s]mXp-hmb \nKa-\-¯n\v Dt]m-Zv_-e-I-amWv Bcy-`-Sobw \ÂIp¶ At±-l-¯nsâ kztZi kw_-Ô-amb sXfn-hp-Ifpw ssP\-]m-c-¼-cy-¯n-eq-¶nb ]cm-aÀi-§-fpw. ASp-¯-Im-e¯v `qJ-\-\-¯n ssP\-þ-_u-²-]m-c-¼cyw hyà-am-¡p¶ sXfnhp-IÄ N{a-h-«¯v e`y-am-b-Xmbn {io. kn. c[m-Ir-jvW³ Cu teJ-I-t\mSv ]dbp-I-bp-−m-bn. tIc-f-¯nsâ kmwkvIm-cnI ]mc-¼-cy-s¯-¸än IqSp-X hkvXp\n-jvT-amb Hcp ho£-W-¯n\pw tIc-f-¯nse ssP\-þ-_p-²-]m-c-¼-cy¯n\v sshZn-I-]m-c-¼-cy-t¯-¡mÄ ]pcm-X-\-Xz-ap-s−¶v t_m²y-s¸-Sp-¶-Xn\pw Bcy-`S³ Ncn-{X-Im-c-·mÀ¡v t{]c-I-am-Ip-sa¶v Icp-Xmw. Cu teJ-\-¯nsâ c−mw `mKw, Bcy-`-Ssâ kztZiw kw_-Ôn¨ kzX-{´-amb tPymXnx-im-kv{X-]-c-amb At\z-j-Whpw N{a-h«w At±-l-¯nsâ \nco-£W tI{µ-am-bn-cp-¶p-sh¶v Øm]n-¡p¶ hnhn[ sXfn-hp-I-fp-am-Wv.
14
`mKw þ II
Bcy-`-So-b-¯n-eqsS ..... Hcp ]pXnb At\zjWw Bcy-`-So-b-¯n-eq-sS. Bcy-`-So-b-¯nemsI 121 tÇmI§-fm-Wp-Å-Xv. {KÙ-¯nsâ LS\ B[p-\nI ho£-W-¯n C{]-Im-c-am-Wv. 1.
KoXn-Im-]mZw þ Zi-Ko-Xn-I-sb¶v {]kn-²sa¦nepw awK-ft- Çm-I-§fpÄs¸sS 13 tÇmI-§Ä e`y-am-Wv.
2.
KWn-X-]mZw þ 33tÇmI§Ä.
3.
Ime-{In-bm-]mZw þ 25 tÇmI§Ä
4.
tKmf-]mZw þ 50 tÇmI§Ä
BsI 121 tÇmI§Ä. H¶p c−v tÇmI-§Ä {]£n-]vX-§-fm-sW¶v Nne ]mÝm-Xy-]-WvUn-X-·mÀ hmZn-¨n-cp-¶p. B hnhm-Z-¯n-te¡v IS-¡msX Bcy-`So-b-¯neqsS At±-l-¯nsâ kztZiw AYhm \nco-£-W-Øm\w tXSn Hcp ]cy-th-£-W-¯n-\mWv ChnsS {iaw. {Kl-a-[y-a-K-Xn-Ifpw ({`-a-W-kw-Jy-IÄ) A£-c-kw-Jymmkt¦Xhpw \ÂIp¶ Zi-Ko-Xn-Isb AYhm KoXn-Im-]m-Z¯nse 13 tÇmI§Ä¡v Øe-]-c-amb {]k-àn-bn-Ãm-¯-Xn-\m Ahsb amän \nÀ¯n-bm \ap¡v e`n-¡pI BcymjvSiXn F¶v {]kn-²-amb 108 KoX-§fpsS {Xn]-Zn-bmb {KÙ-am-Wv. Ch-bnse aq¶v ]mZ-§-fn KWn-X-]mZhpw tZihp-ambn _Ô-an-Ãm-¯-Xm-Ibm \ap¡v ]cy-th-£-W-¯n-\mbn e`n-¡p-¶Xv Ime-{In-b-bn-sebpw tKmf-¯n-sebpw 75 tÇmI§-fm-Wv. Cu 75 KoX-§-fn Fhn-sS-sb-¦nepw Ah¡v P·w \ÂInb tZi¯nsâ ssIs¿m¸v D−mIpsa¶ hnizmkw am{Xw ssIapXembn þ ]Xn\©p \qäm−pIÄ ]n¶nse B {]Xn`m[\sâ hnNmc[mcbpsS Hcwis¯ km²yambncp¶ \nco£W§sf ASnØm\am¡n DÄ¡®psIm−v ImWphm³ {ian¡pIbmWv.
1. DÖ-bn\o Bcy`S\v A]-cn-Nn-X-tam? Bcy-`-Sm-Nm-cysâ Øe-ta-sX¶ Nn´ a\-Ên s]m´p-t¼mÄ, Hcp imkv{XIm-c³ Bcy-`-So-b-¯n tXSp-I, At±-l-¯n\v Gähpw ]cn-Nn-X-amb Øe§Ä Gh-bm-bn-cp-¶p-sh-¶-Xm-Wv. alm-Im-hy-§-sf-gp-Xnb Imfn-Zm-ksâ Imcy¯n IrXn-I-fpsS _mlpeyw sIm−pw hnh-c-W-§Ä sIm−pw DÖ-bn\o hmknbmWv AYhm amf-h-tZ-io-b-\m-Wv, cma-Kncn kµÀin-¨n-«p−v Fs¶ms¡ \nK-a-\-§-fn-se-¯pI \njv{]-bm-k-am-Wv. 75 Ime-þ-J-tKm-fo-b-K-WnX KoX-§fn A§-s\-sb-´mWv {]Xo-£n-¡p-hm³ Ign-bpI? tKmf]mZw tÇmIw 14 C¯-cp-W-¯n hfsc {it²-b-am-Wv. `mc-Xob tPymXnxim-kv{X-¯nepw Ncn-{X-¯nepw DÖ-bn\o F¶m hnh-£n-¡-s¸-Sp-¶Xv almIm-e-k-¶n-[n-sIm−v {]kn-²-amb alm-\-K-cn-bm-Wv. kqcysâ ]c-a-{Im-´n¡v
15
AYhm `qan-bpsS km¦Â]nI A¨p-X-−nsâ Ncn-hn\v Xpey-amb 240 tcJmwiw sIm−v ]pIÄs]ä Øew. F¶m Bcy-`-S³ ]d-bp-¶-sX-´mWv? ØePea[ymæm `qI£ymbm `th¨XpÀ`mtK DÖbn\o e¦mbmx X¨Xpcwti ktam¯cXx (4-14) ØePea[yamb {[ph¯n \n¶pw `q]cn[nbpsS ImÂ`mKw (3600/4 = 900) ]n¶nSpt¼mÄ e¦bpw e¦bn \n¶pw Sn ]cn[nbpsS ImÂ`mKw, AXmbXv, `q]cn[nbpsS ]Xn\mdnsem¶v (3600/16 = 22.500) Ignbpt¼mÄ DÖbn\nbpw ØnXn sN¿p¶p. `mcXob tPymXnximkv{XNcn{X¯n hnhmZ¯n\v XncnsImfp¯nb Bcy`Ssâ {]kvXmh§fnsem¶mWnXv. Bcy`Ssâ injyKWw BNmcy³ ]dªXv icnsb¶v iTn¨t¸mÄ Ah´nbnse hcmlanlnc\pw ]n¶oSv h¶ {_ÒKp]vX\pw At±l¯nsâ `mcXob tPymXnximkv{X¯nse c−mw I£ybpw Bcy`S³ sXämsW¶v kaÀ°n¡pIbp−mbn. tIcfob\mbncp¶ Bcy`Sob`mjyImc\mb kqcytZh³ (AD 1100\Sp¯v, KwssKsIm− tNmf ]pchmkn) {_ÒKp]vXsâ hnaÀi\s¯ ]n´pSÀ¶v X¨Xpcwti F¶Xn\v ]©Zimwti F¶v amäw hcp¯n DÖbn\nbpsS tcJmwiw 24 Un{KnbmsW ¶v Øm]n¡p¶p. ]n¡me¯v h¶ \oeIWvTtkmabmPn DÖbn\nbpsS hnkvXrXn ImcWw hnhn[ P\]Z§fpÅXmWv Bcy`Ssâ ]cmaÀi¯n\v ImcWsa¶v hniZoIcn¡p¶p.
Cu hnhmZ¯n\v ImcWw Cu hnhmZ¯n\v ImcWw Dulns¨Sp¡phm³ ]Xnaq¶maXv KoX¯nte¡v t\m¡nbm aXn. DZtbm tbm e¦mbmw tkmƒkvXabx khnXptch kn²]ptc a[ymtÓm batImSymw tcmaIhnjtbƒÀ[cm{Xw kymXv "e¦bnse DZb¯n\v kn²]pc¯n AkvXabhpw a[ymÓhpw tcmaI]pcnbn AÀ²cm{XnbpamIp¶p"
batImSnbnÂ
`qa[ytcJsb JWvUn¡p¶ bmtaym¯c tcJIÄ, DÖbn\o tcJ e¦ bneqsS IS¶pt]mIp¶Xp t]mse `q]cn[nbpsS \mensem¶v `mK¯v kn²]pcw, batImSn, tcmaI]pcn C§s\ \mev k¦Â]\KcnIsf tZim´c¯n\v Bkv]Zambn BNmcy³ IÂ]n¡pIbmWv. DÖbn\o tcJ `q a[ytcJsb kÔn¡p¶ e¦m\Kcntbm Ahbn \n¶pw 900 AYhm 15 \mgnI AIe¯n ap³]dª \KcnItfm Hcp Ime¯pw D−mbncp¶nÃ. `qan¡v A£hpw a[ytcJbpw k¦Â]n¡p¶Xp t]mse KWnXþBibmh XcW kuIcy¯n\pambn tPymXnximkv{Xa·mÀ \S¯nb IÂ]\ am{XamWv Cu \KcnIÄ. 22.50 D¯c A£mwi¯nÂ, e¦bn \n¶pw `q]cn[nbpsS ]Xn\mdnsem¶v `mK¯v Bcy`S³ ]dbp¶ DÖbn\o ]e` AYhm
16
hnjphi¦pOmb A©wKpew k¦Â]n¡s¸« e¦t]mse Xs¶bpÅ k¦Â] \KcnbmWv. PymanXob KWnX]camb Øm\¯n\v aqÀ¯cq]w \ÂIn hnh£n¡s¸«Xv am{XamWv. D¯cA£mwiw 24 Un{Knbnse DÖbn\n almImek¶n[nbm Ncn{XmXoXImew apX {]kn²amb \nÝnXØm\t¯mSv IqSnbXmWv. ]e` AhnsS Hcp ImcWhimepw As©¶v \nÝbn¡s¸SpI km²yhpaÃ. {InkvXphn\v ap¼v aq¶mw \qäm−n NmWIysâ Imew apX i¦pOmbmKWnXw `mcX¯n {]kn²hpw hywKpew apXemb kq£va GII§Ä \nehnencn¡pIbpw sNbvXncp¶Xn\m ]e`bn 20 hywKpew \yq\X km²yamÃ.
NcJWvU§Ä Bcy`S\v \ÂIp¶ km[qIcWw Bcy`S³ \ÂIp¶ A£mwiw icnsb¶v kaÀ°n¡phm\pXIp¶ sXfnhv alm`mkvIcobw III.8 \ÂIp¶p. Bcy`S]mc¼cy¯n tajmZn cminIfpsS NcJWvU§Ä hyXykvX A£mwi§fnteXp ImWp¶Xn\v D]tbmKn¨n cp¶ kq{Xw ChnsS `mkvIc³þI hyàam¡p¶Xv þ ]e` 1 \v NcJWvUw x ]e` (Øm\obw) F¶mWv. ]e` F¶m hnjphÑmb. hnjpZn\¯n ]{´−wKpew DbcapÅ i¦phnsâ a²ymÓOmbbmWv ]e`. ]e` 1 \v A£mwiw 4046'30" Dw NcJWvU§Ä tajþhrj`þanYp\ {XntImW§Ä ¡v bYm{Iaw 240, 192, 81 ChbmIp¶p. Xmsg \ÂIp¶ ]«nIbn \n¶pw A£mwiw A\pkcn¨v D−mIp¶ hyXymkhpw ap³]dª kq{X¯nsâ D]tbmKhpw a\Ênem¡mw. ]e`
A£mwiw
1.00 2.00 2.30 3.00 4.00 5.00 5.00 5.30 5.72 6.00
4.76 9.46 10.85 14.04 18.43 22.50 22.62 24.00 25.50 26.57
NcJWvUw taSw CShw anYp\w 238 476 547 714 952 1183 1190 1271 1362 1428
193 387 444 580 773 961 966 1033 1106 1160
79 158 182 237 316 393 395 422 452 474
240N A£mwiamb bYmÀ° DÖbn\n¡mWv ]e` 5 IÂ]n¡p¶sX¦nÂ
NcJWvU§fnepw X¶nan¯w KWn¡s¸Sp¶ cmiypZb§fnepw KpcpXc amb \yq\XbmWv ^ew. `mcXobtPymXnximkv{X]mc¼cy¯n ]e` A©mb \Kcnsb DÖbn\nsb¶v Bcy`S³ hnfn¨Xv icnbmb DÖbn\n sb¸än Xn«anÃmXncp¶XpsIm−mWv. 240N A£mwiamb bYmÀ° DÖbn
17
\n¡v ]emwKpew A©mbn Bcpw IÂ]n¡pIbnsöpw ]e` hywKpew kq£vaambn \nÀ®bn¡p¶ ØnXnbn am{XamWv apIfnse KpW\kq{Xw km[phmIpI F¶pw ]«nIbn \n¶pw hyàamWv. Ipkpa]pc¯v 25030' Xmakn¨ncp¶ Bcy`S\v DÖbn\n 240N Xn«anÃmsX hcnIbnÃ. AYhm Ipkpa]pc¯v (25030') hkn¨ Bcy`S\v DÖbn\nbpsS ]emwKpew 5:00 Bbncp¶psh¦n Ipkpa]pc¯n\v F{X kq£vaambn ]e` \nÝbncn¡pw? Cu KpW\kq{Xw Gähpw kq£vaw Ipdª tcJmwi§fnembncn¡pw F¶ hkvXpXbpw ]emwKpew H¶mb Øew tIcf¯n\pw sX¡v ISenemIpIbpw sN¿p¶Xn\m Cu kq{X¯nsâ bYmÀ° DÛhw ]e` 2.3 Bb N{ah« ¯msW¶pw AXn \n¶pw ]e` H¶mb Øes¯ NcJWvU§sf lcn¨v \nÀ®bn¡bmWv sNbvXsX¶pw \ap¡v a\Ênem¡mw. ]e`
A£mwiw
2.30 1
10.85 4.76
NcJWvUw taSw CShw anYp\w 547 238
444 193
182 79
tIcf¯n \nco£n¨v \nÀ®bn¨ aqeyw D]tbmKn¨v ]e` H¶mb Øm\ ¯n\v NcJWvU§Ä KWnX]cambn Is−¯pIbmWv Bcy`S]mc¼cy ¯nep−mbXv. a[ytIcf¯n ]e` c−msW¶Xv {i²nt¡− ImcyamWv. D¯ctZi¯nse Øqeamb ]emwKpe§fn \n¶pw apIfn \ÂInb kq{Xw Dcp¯ncnbpI km²yambncp¶nÃ. DZmlcW¯n\v ]e` A©mbn IcpXn {_ÒKp]Xv³ DÖbn\nbpsS NcJWvU§fn \n¶pw ]e` H¶nsâ NcJWvU§Ä \nÀ®bn¨m e`n¡pI þ ]e`
A£mwiw
5 1
24.00 4.76
NcJWvUw taSw CShw anYp\w 1271 254
1033 207
422 84
Øqeamb ]emwKpehpw \nco£W]canXnIfpap−mbncp¶ ImeL«¯n ]e` sIm−pÅ KpW\w hgn NcJWvUw \nÀ®bn¡p¶ KWnX]co£Wþ \nco£W§Ä tIcf¯n Xs¶bmWv P·w sIm−ncn¡pI. Ipkpa]pc¯v ÇmLn¡s¸Sp¶ PvRm\w F¶v Xsâ IrXnsb¸än \m¸¯nbmdmw hbÊn  (Ien 3600  23 hbÊv, 3623  hbÊv 46) tcJs¸Sp¯phm³ IgnªXv AXn\memWv.
240N-- DÖbn\o \Kcn Bcy-`-S\v ]cnNnXambncp¶nà Bcy`Sob cN\mIme¯v Bcy`S\v DÖbn\o P\]Zw ]cnNnXambncp¶nsà ¶v CXn\m hyàamIp¶p. D¯c`mcX¯nse hcmlanlnc\pw {_Ò Kp]vX\pw ]n¡me¯p−mb hnaÀi\§fpw Cu [mcW¡v Dt]mZv_e IamIp¶p. DÖbn\o A£mwiw kw_Ôn¨v hnhmZw \ne\ns¶¦nepw tc
18
Jmwiw kw_Ônt¨m, bmtaym¯c tcJ kw_Ônt¨m bmsXmcp hnhmZhpw D−mbncp¶nÃ. e¦þDÖbn\o kabtcJ¡v Ingt¡m ]Snªmtdm Bb Xsâ tZi¯n\v Ahiyamb tZim´c kwkvImcs¯¸än Bcy`S³ kqNn¸n ¡p¶panÃ. e¦þDÖbn\o bmtaym¯ctcJbn DÖbn\o P\]Z¯n \n¶pw AIse Z£nW`mK¯mbncp¶p Bcy`Ssâ Øesa¶v CXn \n¶pw a\Ênem¡mw.
Ipkpa]pcw, D¯cA£mwiw 25N40, tcJmwiw 85E15 DÖbn\n 24 Un{Knbnse P\]Zw ]cnNnXasæn F§s\bmWv H¶c A£mwiw IqSpX D¯camb Ipkpa]pcw Bcy`S\v ]cnNnXamIp¶Xv? AXpt]mse, Ipkpa]pchmknbmb (25N40) Bcy`S\v DÖbn\n (240N) Xn« anÃmsX hcp¶sX§s\? bmtaym¯ctcJt\m¡nbm DÖbn\n¡v ]¯v Un{Kntbmfw AYhm Bcy `Ssâ `q]cn[nam\w A\pkcn¨v GXm−v F¬]Xv tbmP\tbmfw Ing¡mWv Ipkpa]pcw. Ipkpa]pcs¯ \nco£W§Ä¡v F¬]Xv tbmP\bpsS tZim´cw \ÂImsX kn²m´IÂ]\ km²yambncp¶nÃ. Xsâ tZihpw Ahew_amb bmtaym¯ctcJbpw X½nepÅ LSnImhyXymkw GsXmcp tPymXnximkv{XÚ\pw tcJs¸Sp¯pI Xs¶ sN¿p¶XmWv. kqcytZh \pw, ]ctaizcmNmcycpw aäpw X§fpsS Øew DÖbn\o tcJbpambn X§ fpsS Øe§Ä¡p−mbncp¶ hyXymkw hyàambn ]dªncn¡p¶Xv {i²n ¡Ww. Ipkpa]pc¯v (25N40) Pohn¡p¶ Hcp tPymXnximkv{XÚ\v hfsc ASp¯ A£mwiapÅ Ab\m´tcJbnse DÖbn\nbpambpÅ tZim´c hpw aäpw hyàam¡msX 80 tZim´ctbmP\ItfmsS DÖbn\n bmtaym¯c tcJ Bkv]Zambn kn²m´w cNn¡pI km²yambncp¶nÃ. Ab\m´tcJ¡v (Tropic of Cancer) hS¡pÅ Ipkpa]pc¯mWv Bcy`S³ Pohn¨ncp¶sX¦nÂ, Ab\m´tcJ¡v sX¡pw hS¡pw kqcy³ \ng hogv¯p¶XnepÅXpw i¦pOmbbnepÅXpamb hyXymks¯¸än At±lw ]dbmXncn¡pI F¶Xpw km[mcWKXnbn hnNn{Xambn tXm¶p¶p.
2. `q]cn[n hnhmZhpw Xt±iob kv]jvS`q]cn[nbpw DÖbn\nbpsS A£mwiw t]mse Xs¶ Bcy`S³ \ÂIp¶ `q]cn[nbpw hnhmZ]camWv. kqcykn²m´hpw {_ÒKp]vX {]`rXnIfpw 1600 tbmP\ bSp¯v hymkhpw 5000 tbmP\bSp¯v `q]cn[nbpw \ÂIpt¼mÄ Bcy`S³ \ÂIp¶ hymkw 1050 tbmP\bpw At±l¯nsâ ss]þaqeya\pkcn¨v π = 3.1416, ]cn[n 3299 tbmP\bpamWv. DÖbn\oþe¦ Zqcw `q]cn[nbpsS ]Xn\mdnsem¶mIbm 206 tbmP\bmsW¶pw e`n¡p¶p. `mcX¯nse Xs¶ hnhn[ tPymXnximkv{X·mÀ `qhymk]cn[nIÄ¡v hyXymkvX§fmb aqey§fpw hyXykvX§fmb e¦þDÖbn\o, e¦þIpcpt£{Xw, e¦þ I\ym Ipamcn Zqc§fpw \ÂIp¶ sshcp²yw `mcXob tPymXnximkv{X ]mc¼cy ¯n ImWp¶p. Cu sshcp²y¯n\v ImcWw tPymXnximkv{XÚ·mÀ
19
kztZiobamb kv]jvS`q]cn[n X§fpsS CÑm\pkrXambn 360 sâ KpWnXambn kzoIcn¡p¶psh¶XmWv. Bcy`Ssâ injy·mcpw ]mc¼cyhpw Bcy`Sob aqeyw Xs¶ kzoIcn¨Xn\m Cu X¯z¯nsâ km[pX ]cntim[n¡p¶Xn\v CXc tPymXnximkv{X·mÀ \ÂIp¶ `q]cn[n aqey§sf B{ibnt¡−nbncn¡p¶p. Xmsg \ÂIp¶ ]«nI Cu hnjb¯n aXnbmb hnhc§Ä \ÂIp¶p. Cdmt«mkvsX\oknsâ `q]cn[n aqey§Ä temIimkv{XNcn{X¯n Xs¶ hnhmZhnjbamWv. 216000, 252000 C§s\ c−v aqey§Ä AeIvkm{−nb bn ]pcmX\Imew apX tÌUnb F¶ GII¯n \nehnencp¶p. Chsb A¼XpsIm−v lcn¨m In«p¶ tbmP\IfmWv apIfn \ÂInbncn ¡p¶Xv. 310 A£mwiamWv Cdmt«mkvsX\okv AeIvkm{−nb¡v \nÀ®bn ¨ncp¶sX¶v tcJIÄ kqNn¸n¡p¶p. 252000*Cos 310 = 216000 F¶ bpàntbmsS kztZikv]jvS`q]cn[n Cdmt«mkvsX\okv 252000 tÌUnb F¶v \nÝbn¡pIbmWv sNbvXsX¶v CXn \n¶pw a\Ênem¡mw. tbmP\bpsS IW¡n `qa[yamb e¦¡pw AeIvkm{−nb\Kc¯n\pw bYm{Iaw kv]jvS`q]cn[n 360x14, 360x12 F¶ bpàntbmsS tbmP\ \nÝbn¨XmsW¶v ChnsS hyàamIp¶p. imkv{XÚ³
C=2πr at 00/φ
kztZiob tbmP\
Cosφ = Y*360/C
A£mwiw φ
Cdmt«mkvsX\okv
4320 5040
12
0.86
31.0
9
0.98
10.85
13.5
0.98
10.82
13
0.94
20.61
13
0.94
19.57
10
0.92
23.55
8.5
0.92
22.50
8
0.9
25.84
Bcy`S³
{_ÒKp]vX
`mkvIc³þII
htSizc³ apÖe³
3240 3299 4860 4948 4680 5000 4680 4967 3600 3927 3060 3311.24 3240
Øew AeIvkm{−nb `qa[yw þe¦ s]m¶m\n `qa[yw þe¦ s]m¶m\n `qa[yw þe¦ `nÃae `qa[yw þe¦ _nUv `qa[yw þe¦ DÖbn\n `qa[yw þe¦ DÖbn\o `qa[yw þe¦ {]Imiw
20
hcmlanlnc³
3600 4320 4800 2880 3200
`qa[yw þe¦
12
0.9
25.84
8
0.90
25.84
{]Imiw `qa[yw þe¦ Ipkpa]pcw `qa[yw þe¦
Bcy`S³ Bcy`Sob¯n \ÂInb `q]cn[nbmb 3299 tbmP\¡v B[mcw bYmÀ°¯n Xsâ \nco£WtI{µambncp¶ s]m¶m\n (N{ah«w) (A£mwiw 10N51) ¡v \nÝbn¨ 360x9 = 3240 F¶ ]cnamWw BIp¶p. Xsâ AÀ²cm{Xn]£¯n kzoIcn¨ 4948 epw s]m¶m\nbpsS 360x13.5 = 4860 F¶ bpànbpw kzm[o\hpw ImWmw. ChnsS \nÀ®bn¡s¸«ncn¡p¶ A£mwiw 10N51 DÖbn\nbpsS bmtaym¯ctcJ tIcfXocs¯ JWvUn ¡p¶Xpw `mcX¸pg ISen ]Xn¡p¶Xpamb ØeamIp¶p. s]m¶m\n þN{ah«w taJebnemWv Bcy`S³ Pohn¨ncp¶sX¶v CXn\m hyàamIp ¶p. {_ÒKp]vXsâ Imcy¯n At±l¯nsâ `q]cn[naqeyw `nÃae(20N37)bn 360x13 = 4680 tbmP\ F¶ aqeyw \ÂIp¶p. \nehnencn¡p¶ k¦Â] §f\pkcn¨v {_ÒKp]vX³ cmPØm\nse au−v A_p AYhm AÀ_pZKncn¡v hS¡v {ioa AYhm `nÂa F¶v ]n¡me¯v Adnbs¸« Ab\m´tcJbnepÅ (23-240N) Øe¯v Pohn¨ncp¶Xmbn IcpXs¸Sp¶p. CXv icnbÃ. {_ÒKp]vXsâ Imeamb {InkvXphn\v tijw Ggmw \qäm−n D−mbncp¶Xpw `nÃae F¶ aqe\mat[bapffXpamb Øew \À½ZbpsS sX¡v Z£nWKpPdm¯nepÅ `nÃaebmWv. `mkvIc³ -II HudwK_mZn\Sp¯v _nUnemWv Pohn¨ncp¶sX¶pw ]n¡me ¯v DÖbn\nbnte¡v hmkw amänbXmbpw kqNn¸n¡p¶ c−v aqey§Ä \ÂIn ImWp¶p. hcmlanlnc³ Ipkpa]qcw Ahew_ambn kzoIcn¨Xm bpw \ap¡v a\Ênem¡mw. Bcy`Ssâ injy]mc¼cy¯n s]« htSizc³ {_ÒKp]vXsâ hnaÀi\ §Ä¡v \ninXambn adp]Sn ]dªbmfmWv. At±l¯nsâ aqeyw {i²nt¡ −XmWv þ 3311.24 tbmP\ F¶ aqey¯n\v ASnØm\amb bpàn 360x8.5 = 3060, Bcy`S³ \ÂIp¶ DÖbn\nbptSXmWv. Cu hkvXpX Bcy`Ssâ A£mwiw \nÀ®bn¨ bpànbpsS km[pX¡v ]qÀ®amb km[pX \ÂIp¶p. aRvPpf AYhm apÖe³, {]Imi]pc¯nse kqcy\mamhmb tPymXnx imkv{XÚ³ `q]cn[n¡v \ÂInb c−v kzX{´aqey§fpw At±l¯nsâ kztZiamb {]Imi]«W¯nsâ A£mwiw kqNn¸n¡p¶p.
21
`q]cn[n¡v kzX{´amb aqeyw \ÂInb FÃm tPymXnximkv{XÚ·mcpsS bpw kztZiw kw_Ôn¨v icnbmb kqN\ apIfn \ÂInb bpàn \ÂIp ¶Xn\m Bcy`Ssâ kztZiw s]m¶m\n AYhm s]m¶m\n¡Sp¯ ssP\tI{µamb N{ah«ambncp¶psh¶v hyàamIp¶p. N{ah«¯¸³ (imkvXmhv) ssP\]mc¼cyw kqNn¸n¡p¶psh¶ A`yql§fpw Bcy`Ssâ ssP\kzm[o\w kqNn¸n¡p¶ Ime{Inb H³]Xmw tÇmI¯nse DÕÀ¸nWn, A]kÀ¸nWnbmZnbmb bpKLS\bpw _Ôs¸Sp¯n Nn´n¨m N{ah«w Bbncp¶p Bcy`Ssâ tZiambncp¶psh¶v Dd¸n¡mw. tKmf]mZw, tÇmIw 11 C¯cpW¯n hfsc {it²bamWvþ tacpÀtbmP\am{Xw {]`mItcm lnahXm ]cn£n]vXx \µ\h\ky at[y cXv\abx kÀÆtXm hr¯x (4 -11) tacp IjvSn¨v Hcp tbmP\bmWv F¶v Bcy`S³ ]dbp¶p. ]e hymJymImc ·mcpw Cu {]kvXmhw tacphnsâ Dbcambn hymJym\n¨ncn¡p¶p. \oeIWvT ³ ]dbp¶phs{X, ]pcmW§fnse k¦Â]§sf (84000 tbmP\ Dbcw AXn  16000 `qan¡pÅn apXemb {]kvXmh§Ä) JWvUn¡phm³ ]dbp¶Xm Ws{X. Cu {]kvXmh¯n Bcy`S³ \ÂIp¶Xv tacphnsâ NpäfhmWv. `qanbpsS A£w tacp]ÀÆXamIbm AhnsS A£mwiw 90 Un{KntbmfamWv. 00e¦ bn `qanbpsS Npäfhv 3299 tbmP\ BIpt¼mÄ 900tZhtemIamb tacphnsâ ]cn[n F{XbmIpw? 900bpsS tImSnPymhv ]qPyamsW¶v hyàw. A£mwiw AÂ]w Ipdªv 89058'57".48 BsW¶v IcpXnbmtem? AXmbXv Hcp Ie IpdhmWv tacphnsâ ]cn[nbpsS A£mwiw F¶v IcpXnbm 3299x Cos 89059' = IjvSn¨v Hcp tbmP\ F¶ D¯cw \ap¡v e`n¡p¶p. 3299x Cos 10051' = 3240 F¶v kztZi¯n\v kv]jvS`q]cn[n \nÝbn¨ bpàn
Xs¶ Bkv]ZambmWv Bcy`S³ tacpÀtbmP\am{Xw F¶v {]Jym]n¨Xv. Cu {]kvXmhw tacphnsâ NpäfhmsW¶v ]n¡me hymJymImc·mÀ a\Ênem¡pI D−mbnÃ. `mkvIcsâbpw tkmtaizcsâbpw hymJym\¯n t]mepw Cu hkvXpX shfnhmIp¶nsöXmWv hnkvabIcw.
3. kqcysâ A{Kw, tKmf]mZw tÇmIw 31Â sXtäm? {_Ò-Kp-]vX\pw aäpw Bcy-`-S-\n-em-tcm-]n-¡p¶ \yq\-XI - -fn-sem-¶mWv tKmf]mZw tÇmIw 31se hnjbw. ]cam]{IaPohmanjvSPymÀ[mlXmw XtXm hn`tPXv Pymew_tI\ e_v[mÀIm{Km ]qÀÆm]tc £nXntP (30) km hnjphtÖym\m tNXv hnjphZpZ¥w_tI\ kwKpWnXm hnjphPybm hn`àm e_v[x ]qÀÆm]tc i¦px (30)
22
kqtcymZbmkvXab§Ä¡v N{Ihmf¯n ]qÀÆþ]ÝnatcJbn \n¶papÅ hyXnbm\amb A{Kw AYhm ZnKwiw KWn¡p¶sX§s\sb¶v tÇmIw 30 ]dbp¶p. kqcysâ `pPPymhns\ (Rsine λ) ]ca{Im´nPymhv (Rsine ω) sIm−v KpWn¨v A£mwitImSnPymhv AYhm kztZiew_Iw (Rsine 90-φ) sIm−v lcn¡p ¶Xv A{Kw. i.e. α = (Rsine λ) *(Rsine ω) /(Rcosφ) XpSÀ¶v tÇmIw 31  ]dbp¶Xv þ B A{Kw A£Pymhnt\¡mÄ Ipdhmbncn¡pIbpw kqcy³ D¯cmÀ²tKmf¯nembncn¡pIbpw sN¿pt¼m Ä kqcy\v ]qÀÆþ]ÝnatcJbnepÅ D¶Xmwiw (prime vertical altitude of the gnomon) A{Ks¯ kztZiew_Iw sIm−v KpWn¨v A£Pymhv sIm−v lcn¨m e`n¡p¶XmWv. i.e i.e. Rsine h = α* (Rcosφ /Rsineφ). Bbnc¯n\m\qdntesd hÀj§fmbn {_ÒKp]vXsâ Imew (AD629) apX \ne\n¡p¶ hnaÀi\w C´y³ \mjW kb³kv A¡mZan ASp¯ Ime¯v ]p\x{]kn²oIcn¨ncn¡p¶X\pkcn¨v A{Kw A£Pymhnt\¡mÄ Ipdhmbncn¡Ww F¶ Bcy`Sbpàn {]amZamWv. A{Kw A£Pymhnt\ ¡mfÃ, {Im´nPymhnt\¡mfmWv Ipdtb−Xv F¶v {_ÒKp]vX³ Xncp¯n bXv \qäm−pIfmbn BhÀ¯n¡s¸Sp¶p. alm`mkvIcob¯n Bcy`Ssâ {]amWw BhÀ¯n¡s¸«n«p−v. ]n¡m es¯gpXnb eLp`mkvIcob¯n {]amWw icnbmbn \ÂIp¶Xmbn ]WvUnX·mÀ ]dbp¶p. ]s£, tIcfob\mbncp¶ `mkvIc³ D¯c `mcX¯nse hÃ`nsbse¯nb tijamWv Cu amäw hcp¯nbncn¡pI F¶v Xmsg \ÂIp¶ hkvXpXIÄ kqNn¸n¡p¶p.
tÇmIw 31 Dw hnaÀi\hpw Bcy`S³ tIcfobs\¶v Øm]n¡p¶p. apIfn ]dª Bcy`Sob tÇmIw km[phmsW¶v Xmsg \ÂInbncn¡p¶ ]«nIbn \n¶pw a\Ênem¡mw. kuIcy¯n\mbn kahmIy§fpw {]XoI §fpw Cw¥ojn \ÂInbncn¡p¶p. XpSÀ¶pÅ NÀ¨bn {XntImWanXnbp sS X¯peyamb kwkvIrX]Z§Ä D]tbmKn¡m³ {ian¨n«p−v. AhyàX tXm¶p¶psh¦n _Ôs¸« kahmIyw ]«nIbn \ÂInbncn¡p¶Xv A\p kcn¨v NÀ¨ a\Ênemt¡−XmWv. Bcy`Ssâ tZiw tIcfamsW¶Xn\v Gähpw iàamb, A\ntj[yamb, sXfnhmWv Cu tÇmIhpw AXn\v ]n¡me¯p−mb hnaÀi\§fpw. A{Kw \nÀ®bn¡p¶ kq{Xw Rsin agra = Sinδ/Cosφ {i²n¡pI. δ kqcy{Im´n A£mwit¯¡mÄ (φ) A[nIcn¡pt¼mÄ am{Xta D¶Xmwiw Hcp Øe¯v e`yamIp¶pÅp. δ = φ BIpt¼mÄ e`yamIp¶ A{Khpw A£mwiPymhpw
23
φ
kqcy {Im´n δ
A£mwiw
]«nIbn hnhn[ A£mwi§Ä¡v \ÂInbncn¡p¶p. A£mwiw Ipdhmb Øe§fn A{KPymhv A£mwiPymhn\v GXm−v XpeyamWv. A{Khpw {Im´nbpambpÅ hyXymkhpw IpdhmsW¶Xn\mepw δ = φ BIpt¼mÄ {Im´n = A{Kw = A£mwiw F¶ kmlNcyw Xmgv¶ A£mwiamb Øe§fn \ne\n¡p¶Xn\m Bcy`S³ A£mwi Pymhns\bpw A{Ks¯bpw ASnØm\am¡n D¶Xmwiw e`yamIp¶ Imew Xsâ A£mwi¯n\v \nÀÆNn¡pIbmWp−mbXv. i¦pOmbmKWnX¯n A£mwihpw ]emwKpehpw Gähpw ASnØm\LSI§fmbXpsIm−mWv Bcy`S³ A{KPymhns\ A£mwihpambn _Ôs¸Sp¯n {]amWw \ÂInb Xv.
Rsinφ
Sin δ/Cosφ = Agra in Degrees Rsin agra
Rsin agra Agra-δ - Rsinφ
3
3
179.93
180.17
3.004
0.24
0.00
6
6
359.37
361.33
6.033
1.96
0.03
9
9
537.82
544.49
9.113
6.67
0.11
10.85
10.85
647.16
658.90
11.050
11.74
0.20
12
12
714.8
730.72
12.272
15.92
0.27
15
15
889.82
921.15
15.542
31.33
0.54
18
18
1062.4
1117.00
18.961
54.60
0.96
21
21
1232.1
1319.64
22.573
87.57
1.57
24
24
1398.4
1530.60
26.438
132.24
2.44
sXsä¶v {_ÒKp]vX{]`rXnIfpw B[p\nI KthjIcpw hymJym\n¨ Cu tÇmIw Bcy`S³ tIcfob\msW¶Xn\v Ak¶nKv²amb sXfnhmWv.
4. Bcy-`-So-b-c-N\¡v ASn-Øm-\-amb kqcy-N-{µ-{K-l-W§fpw JtKm-fob-\n-co-£-W-§fpw Bcy-`-S³ IS-en t]mbn kqcy{KlWw \nco£¨-Xmb sFXnlyw cmtPjv sIm¨À Xsâ `mc-Xo-b-tPym-Xnx-im-kv{X- kw-_-Ô-amb teJ-\-¯n tcJ-s¸-Sp¯n-¡m-Wp-¶p. {]mtZ-in-I-amb JtKm-fob \nco-£-W-§-fn Gähpw {][m-\s¸-«-XmWv kqcy-{K-l-W-¯nsâ \nco-£Ww. {Kl-K-Wn-X-¯nsâ, kn²m-´-§ fpsS kq£va-X-bpsS Dc-IÃv Xs¶ {KlWw {]h-Nn-¡p-I, {Kmk-þ-a-[y-þ-tam-£-
24
Im-e-§Ä IrXy-ambn KWn-¡pI F¶o KWn-X-{In-b-I-fm-Wv. AXp-sIm−v Xs¶ GsXmcp kn²m-´-¯n-sâbpw cq]-s¸-Sp-¯-en kn²m-´-Im-c\v \nco£n-¡p-hm³ Ignª {Kl-W-§Ä¡v henb kzm[o-\-ap-−v. Ae-Ivkm-{−n-bbnse (b-h-\-]p-cn) {]kn² tPymXnx-im-kv{X-Ú-\mb t¢mUn-bkv tSmfan \qäm-−p-I-fpsS _m_n-tem-Wn-b³ {Kl-W-þ-{K-l-\n-co-£W - -tc-J-Isf ASn-Øm\-am-¡n-bmWv Xsâ KWn-X-]-²-Xn¡v cq]w \ÂIn-b-sX¶ hkvXpX hfsc {]kn-²-am-Wv. ]Xn-\©mw \qäm-−nsâ a[y-Im-e¯v ]c-ta-iz-cm-Nm-cyÀ Zr¤WnX cq]o-I-c-W-¯n 51hÀjw \nfm-Xo-c¯v (`c-X-¸p-g) -bpsS Xoc¯v \S¯nb {Kl-W-þ-{K-l-\n-co-£-W-§Ä D]-tbm-K-s¸-Sp-¯n-bn-cp-¶p. \oe-I-WvTtkm-a-bm-Pnbpw KWn-X-]-cn-jvI-c-W-¯n\v \S-¯nb \nco-£-W-§Ä Xsâ IrXn-I-fn NÀ¨ sNbvXn-«p-−v. Bcy-`-S-s\-¸än \oe-I-WvT-tkm-a-bmPn ]d-bp¶Xv {i²n-¡p-I.14 tKmf-]m-Zw, tÇmIw 48 se ]Z-{Xbw sIm−v kI-e-\n-co-£-W-bp-àn-Ifpw Bcy-`-S³ ]d-ªn-cn-¡p-¶p. Bcy-`-So-b-¯nse kq{X-§Ä \nco-£-tWm-]-tbmKn-I-fmb bpàn-Isf DZm-l-cn-¡p-¶-h-bm-Wv. Bcy-`-So-b-¯nsâ kmÀÆ-eu-InI AwKo-Im-c-¯n\pw D]-tbm-Ky-X¡pw CXc kn²m-´-§-tf-¡m-fpÅ t{ijvTX¡pw ASn-Øm\w \nco-£-W-]-T-\-§Ä¡v AXv \ÂIp¶ Du¶-em-Wv, AÃmsX {`a-W-kw-Jy-IfÃ. {Kl-W-þ-{K-l-\n-co-£-W-§-fpsS Cu ]Ým-¯ew Bdmw \qäm−v apX-se¦nepw tIc-f-¯n kPo-h-am-bn-cp-¶p-sh¶v Bcy-`-So-bm-[n-jvT-amb tPymXnx-imkv{X-]m-c-¼cyw kqNn-¸n-¡p-¶p. N{a-h-«-¯n-\-Sp¯ s]m¶m\n ]pcm-X\ Xpd-apJhpw Ad_nI-fpsS hym]m-c-tI-{µ-hp-am-bn-cp-¶-Xn-\m Ae-Ivkm-{−n-b-bnsebpw _m_n-tem-Wn-b-bn-sebpw tPymXnx-im-kv{X-hn-Úm\w ssP\-]m-c-¼-cy¯n A`n-hr-²n-s¸« KWn-X-hp-ambn tNÀ¯v `mc-X-¯n \qX-\-amb Hcp KWn-X-þ-\n-co-£-W-_-²-amb kn²m-´-¯n\v cq]w \ÂIp-I-bmWv Bcy-`-S³ sNbvX-Xv. Cu hkvXp-Xsb km[q-I-cn-¡p¶ Gähpw {it²-b-amb JtKm-fob {]Xn-`m-k-§Ä¡v Bcy-`-Ssâ Ime¯v N{a-h-«hpw tIc-fhpw thZn-bm-bn-cp-¶psh¶v B[p-\nIKWnX kt¦-X-§fpw Ata-cn-¡³ _ln-cm-Imi kanXn (\mk) \ÂIp¶ {Kl-W-hn-h-c-§fpw ASn-Øm-\-am¡n \ap¡v a\-Ên-em-¡mw. Bcy-`-So-b-¯nsâ cN-\m-Im-e-sa¶v hn{ip-X-amb KX-Ien 3623 (CE 522) ASnØm-\-ambn t\m¡n-bm aq¶v hÀjw ap¼v, AXm-bXv KX-Ien 3620  (CE 519) c−v {it²-b-amb kqcy-{K-l-W-§Ä¡v N{a-h«w thZn-bm-bn-cp-¶p-sh¶v ImWmw. (1) Ien 3619 Ipw`-am-k-¯n N{a-h-«¯v (10N51, 75E45) ]qÀ® kqcy-{K-lWw (2) Ien 3620 Nn§-amkw, Z£n-W-tI-c-f-¯n a−-¡m«v `KhXn t£{X-¯n\v kao]w IS-en ]qÀ®-h-e-b-{K-l-Ww. Cu {KlWw N{a-h«¯v `mKn-I-ambn Zriy-am-bn-cp-¶p. Cu {Kl-W-\n-co-£W - -§Ä Bcy-`-So-b-¯nse-§s\ {]Xn-^-en-¡p-¶p-sh¶v Xmsg hyà-am-¡p-¶p. 14
tPymXnÀao-amw-km, \oe-I-WvT-tkm-a-bm-Pn, tUm.-sI.hn. iÀ½-bpsS Bap-Jt¯mSpw hni-Zo-I-c-W-§-tfmSpw IqSn {]kn-²o-I-cn-¨-Xv. s\{lp ¹m\-sä-dnbw {]kn-²o-I-cn¨ A Source Book of Indian Astronomy bnepw \oe-I-WvT-tkm-a-bmPn-bpsS A`n-{]mbw D²-cn¨p ImWmw.
25
N{a-h-«¯v (10N51, 75B45)bnse ]qÀ®kqcy{KlWw 15 s^{_phcn AD 519 Cu {KlW¯nsâ OmbmKXn Fkvs]\mIv \ÂIp¶Xv Xmsg \ÂIp¶p. ]Sw hep-Xm-bmWv {]kn-²o-I-cn-¡p-¶-sX-¦n Nn{Xw sIm−v Xs¶ \ap¡v t_m²y-s¸Smw {KlWw tIc-f-¯n ]qÀ®-ambncp-¶p. tKmf-¯nse tcJm-Nn{X-¯nsâ a[y-¯n \oe-\n-d-¯n AYhm AÂ]w I«n-IqSn ImWp¶ tcJbmWv ]qÀ®-{K-l-W-¯nsâ ]mX. DÖ-bn\o bmtaym-¯c tcJ tIc-f-¯nsâ ]Ýn-a-Xo-cs¯ JWvUn-¡p¶ `c-X-¸pgbpsS ]X\ Øe¯v IqSn-bmWv Cu {Kl-W-¯nsâ ]qÀ®X IS-¶p-t]m-b-Xv.
]pcm-X-\-Im-e¯v {Kl-W-§Ä¡p−m-bn-cp¶ aX-]-chpw D]m-k-\m-]-c-hp-amb {]m[m-\y-¯n\p ]pdsa a[y-Ó-¯n CcpÄ]-c-¯p¶ Cuhn[ {Kl-W-§Ä `oXn-Zhpw tPymXnx-im-kv{X-Ú-·mÀ¡v \nco-£-W-þ-]-co-£-W-§Ä¡v hnc-fambn am{Xw e`y-am-Ip¶ kphÀ®m-hm-k-c-§-fp-am-bn-cp-¶p. jjvSy-_vZm\w jjvSnÀ F¶ KoX-a\p-k-cn¨v KX-Ien 3600 \v ({InkvXp-hÀjw 499) Bcy-`-S\v 23 hb-Êm-bn-cp-¶p-sh-¦n Cu \nco-£Ww km²y-am-bXv At±l¯nsâ 43-
26
mw hb-Ên-em-Wv. XpSÀ¶pÅ c−v-þ-aq¶v hÀj-§-fnse \nco-£-W-]-co-£-W§fpw ASn-Øm-\-am-bmWv HuZ-bnIkn²m-´-¯n\v (e-t¦m-Zbw ASn-Øm-\amb Bcy-`-So-bw) ]qÀ®-cq]w \ÂIn-b-sX¶v A\p-am-\n-¡mw. bpKmZnbmbn
44774 Nm{µamkm´yw Ipdn¨ Aamhmky´yw IenZn\w 1322202.2695 BIp¶p. Bcy`Sobw A\pkcn¨v a[yamhmknbpsS Ahkm\w 12:28 DÖbn\o kabhpw B[p\nIKWnX{]Imcw 12:33 DÖbn\o kabhpw BIp¶p. DÖbn\okabw 14:23 \v {KlWw ]qÀ®hpw ]qÀ®XbpsS ssZÀLyw 8 hn\mgnIbpw Bbncp¶p.
a[yaw a[yaw {Klkv^pSw {Klkv^pSw Bcy`S³ B[p\nIw Bcy`S³ B[p\nIw 0 0 0 kqcy³ 326 20' 326 25' 328 20' 328018' N{µ³ 326020' 326025' 328006' 327058' XpwKw 125038' 125031' --0 0 ]mXw 146 58' 146 58' --{Klw
B[p\nIKWnX¯n\v Gähpw Xpeyamb Cu Bcy`Sob ^e§Ä kqNn¸n ¡p¶Xv Sn {KlW\nco£Ww Ahew_ambn kq£vaam¡s¸« {Kl{`aW kwJyIfmWv Bcy`Sob¯n\v ASnØm\sa¶mWv.
IenhÀjw 3620 Nn§amk¯nse kqcy{KlWw 11 BKÌv 519 AD N{a-h-«¯v \nf-bpsS Ic-bn Zriy-amb ]qÀ®-{K-l-W-¯n\v tijw 177 Znh-k§Ä Ignªv KXIen 3620 Nn§amkw Ccp]Xmw XobXn I\ymIpamcnþ a−¡mSv `mK¯v A£mwiw 08N20  DÖbn\obmatcJbn ISen kqcysâ ]qÀ®-h-e-b-{K-lWw kw`-hn-¡p-I-bp-−m-bn. Cu ]qÀ® heb kqcy{KlWw Bcy`S³ ISen t]mbn ImWpIbp−mbn F¶v Bcy`Sobw kqN\ \ÂIp¶p. Hmcw]än s]m¶m\nbn (Ba¡mhvþN{ah«w) \n¶pw ]mb sI«nb hůn (]mbv¡¸enÂ) I\ymIpamcn¡v \S¯nb Cu bm{X Bcy`Ss\ kw_Ôn¨nSt¯mfw hfsc \nÀ®mbIambncp¶psh¶ hkvXp-XbpsS em©\ Bcy`Sob¯n Zriy-am-Wv. Xmsg ]dbp¶ LSI§Ä hfsc {it²b amWv. (I) e¦þDÖbn\o bmtaym¯ctcJbnse Cu hebþkqcy{KlWw N{µþ XpwKw, ]mXw (cmlp) ChbpsS thKX \nÀ®bn¡p¶Xn\pw ChbpsS bpK{`aWkwJyIÄ ]cnjvIcn¡p¶Xn\pw Bcy`S\v t{]cIambn. N{µ XpwK{`aWthKX Bcy`S³ Iq«n\nÝbn¨Xmbn {_ÒKp]vX³ hnaÀin ¡pIbpw sNbvXp. kqcykn²m´¯n e`yamb {`aWkwJyIsf ]cnjv Icn¨XneqsS Gähpw kq£vaambn XpwKþcmlpKWnXw km²yam¡n
27
F¶v Cu {KlWZnhk¯nse AamhmknbpsS N{µXpwKw, ]mXw Chbp sS a[ya§Ä kqNn¸n¡p¶p. Ien 3620, Nn§w Aamhmkn, 11 BKÌv 519 AD Bcy`S³ B[p\nIw kqcykn²m´w {Klw chn N{µ³ N{µþXpwKw cmlp
140 140 145 137
58 58 20 35
141 140 145 137
00 21 15 36
140 140 140 133
58 58 30 57
kqcykn²m´{]ImcapÅ aqey§Ä B[p\nIaqey§tf¡mÄ F{X Øqeam sW¶Xpw Bcy`Ssâ aqey§Ä F{X kq£vaamsW¶Xpw {i²n¡pI. kqcykn²m´aqey§Ä Xs¶ AÀ²cm{XnI]£¯n Ien 3600 Bkv]Z ambn Bcy`S³ ]cn-jvIcn¨ncp¶Xmbpw Bcy`Ssâ AÀ²cm{XnI kn²m´¯nse {`aWkwJyIfmWv hcm-l-an-ln-c ³ ]©-kn-²m-´n-I-bn kw{K-ln¨ kqcykn²m´¯n \ÂIn-bn-cn-¡p-¶-sX¶pw ]WvUn-X-·mÀ A`n{]m-b-s¸-«n-«p-−v. Cu hmZ-K-Xnsb kaÀ°n-¡p-¶-XmWv Cu {Kl-Whpw KWnX-¯n Cu Xob-Xn¡v B[p-\n-I-K-Wn-X-hp-ambn ZriyamIp¶ \qdv iX-am\w Xpey-X-bpw. B[p-\nI ]mÝm-Xy-K-th-j-Isc hnkva-bn-¸n-¡p¶ Bcy-`-Ssâ kq£va-X¡v Bkv]-Z-amb {Kl-W-\n-co-£-W-§Ä kwi-b-te-i-sat\y ChnsS kn²-am-Ipt¼mÄ kqcy-kn-²m-´-¯nt\m hcm-l-anlncsâ kw{K-l-¯ntem e`y-amb {`aW-kw-Jy-I-fpsS Dd-hnSw hyà-a-Ã. \nco-£-W-]-co-£-W-kn-²-amb Bcy-`-S-aqey-§sf Ah-bpsS kq£vaX a\-Ên-em-¡nb hcm-l-an-ln-c³ kzoI-cn-¨-XmWv ]©-kn-²m-´n-I-bnse kqcy-kn-²m-´-¯n\v BcymÀ²-cm-{X-kn-²m-´-hp-ambn ImWp¶ kam-\-X¡v Imc-Ww. he-b-{K-lWw kw`-hn-¡p-¶Xv N{µ-þ-N-{µ-Xpw-K-þ]mXtbm-Khpw Aam-h-knbpw Hcp-an-¡p-t¼m-gm-Wv. `qan-bn \n¶pw Gähpw AI-e-¯n Xmc-X-tay\ aµKXnbn-e-Ip¶ N{µsâ _nw_-hymkw kqcysâ _nw_-s¯-¡mÄ Ipd-ªn-cn-¡p-¶XmWv ]qÀ®-{K-l-W-¯n sNdp-sX-¦nepw Xo{hamb {]Imihe-b-¯n\v ImcW-am-Ip-¶-Xv. N{µXpwKw cmlp ChbpsS {`aWkwJyIfn Bcy`Sob¯n (3600) hcp¯nbncn¡p¶ Imcyamb amäw kqcy{KlWw (KXIen 3620, 11 BKÌv 519 AD) \nco£n¨Xn \n¶pamsW¶v Xmsg \ÂIp¶ ]«nIbn \n¶pw a\Ênem¡mw. cmlp B[p\nIhpw Bcy`Sob aqeyhpamb hyXymkw Sn {KlWImeamb KXIen 3620 \v sXm«pap¼v KXIen 3620 \v iq\yambn ImWmw. N{µXpwK ¯n\v Cu hyXymkw iq\yamIp¶Xv KXIen 3629 þ3630 hÀj§fnemWv. N{µXpwK¯nsâ Cu sNdnb hyXymkw kmcamt¡−XnÃ. Bcy`Sob¯nse ]cnjvIcn¡s¸« cmlphnsâ KXIen 3619-3620 \pÅ
28
AXnkq£vaX Bcy`S³ Sn kqcy{KlWhpw kao]Ime \nco£W§fpw Bkv]ZambmWv HuZbnIkn²m´¯n\v cq]w \ÂInbsX¶v A\ntj[yambn hyàam¡p¶p. cmlp KXIen B[p\nIw 3590 3596 3600 3608 3612 3616 3618 3619 3620 3623 3636 3646
185 69 352 197 119 42 3 344 325 267 15 182
26 23 1 16 54 32 51 30 10 8 41 16
N{µXpwKw Bcy³ 185 429 352 197 479 402 363 344 325 267 375 182
43 37 12 23 58 34 52 31 9 6 31 0
hyXym B[p\nIw Bcy³ kw -17' -13' -11' -6' -4' -2' -1' 0 1' 2' 10' 16'
168 52 215 180 343 146 227 268 309 71 240 287
29 39 26 59 46 32 55 37 19 24 25 21
168 52 215 181 -17 146 228 268 -51 71 240 -73
51 58 42 11 55 40 2 43 24 27 21 12
hyXym kw -22' -18' -16' 48' -10' -7' 54' -6' -5' -4' 4' 9'
(J) DÖbn\o bmtaym¯ctcJbnse Cu Aamhmkn bpKmZnbmbn 44780maXv kqcybpXnbpw (synodic periods of moon) AlÀKWw iq\ya[yaXnYn¡v (chn = N{µ³) þBcy`Sobw: 1322379.45334, RmbÀ 16:53 UMT (DÖbn\o Øm\obkabw). kqcykn²m´a\pkcn¨v 1322379.72823, 17:29 UMT Ch BIp¶p. HuZbnI]£kn²m´¯nsâ cN\¡v Cu Aamhmkn t{]cI ambn F¶v \ap¡v a\Ênem¡mw. ImcWw {KlWw a[ymÓt¯msS ]qÀ®am b kmlNcy¯n Aamhmkn¡v kqcykn²m´a\pkcn¨pÅ AlÀKWamb 1322379.72823se ssZÀLyw Im Znhkw (0.275) Ipd¨v et¦mZbw Bkv]Z ambn chnþN{µ a[ya§Ä¡pw kv^pS§Ä¡pw hyXymkw IqSmsX KWnXw ]cnjvIcn¡msa¶ bpàn At±l¯n\v tXm¶nbncn¡Ww. (K) kqcykn²m´w Bt]£nIambn t\m¡pt¼mÄ Bcy`Sob¯n Cu {KlWKWnX¯nÂ, a[yaiq\yXnYn aplqÀ¯¯n\pw, aµ^ew aqew kv^pSþAamhmkn¡v D−mIp¶ H¶c\mgnIbpsS Ipdhv C§s\ Zriyam Ip¶ AXoh kq£vaX, Cu {KlWw ZiKoXnIbpsS cN\¡v Ahew_ ambncp¶psh¶v kqNn¸n¡p¶p. (L) N{µew_\w Bcy`Sobhn[n A\pkcn¨v \mw KWn¡pt¼mÄ hfsc IrXyambn Xs¶ {KlWa[yImew e`yamIp¶psh¶Xpw {i²nt¡− kwKXnbmWv. {KlWa[yImew B[p\nI KWnXa\pkcn¨v a[ymÓw Xs¶bmWv. ew_\w Bcy`Sob kq{X§f\pkcn¨v XoÀ¯pw kq£vaamb a[yImew \ÂIp¶p.
29
kabw
DZb
a[y
14:07 13:14 12:41 12:22 12:11 12:04
687.10 671.45 667.23 666.84 667.32 667.91
620.04 247.03 22.01 102.19 171.83 215.12
Zrt£]w
ZrKvPym
Zr¤Xn
ew_\w
Bcy
{_.Kp
607.54 242.28 21.59 100.25 168.56 211.03
1708.32 1020.57 583.11 358.19 270.38 253.03
1596.64 991.40 582.71 343.87 211.40 139.61
24.38 15.14 8.90 5.25 3.23 2.13
53 33 19 11 7 5
58 35 20 12 9 8
Bcy`Ssâ ZrKvPymþZr¤Xn kq{X§sf {_ÒKp]vX³ ]n¡me¯v hnaÀin ¡pIbp−mbn. \Xmwiw D]tbmKs¸Sp¯p¶ Bcy`Ssâ bpàn kap{Z N{Ihmfw Ahew_ambn {Kl\nco£Ww km²yambncp¶psh¶ kqN\ \ÂIp¶p. {_ÒKp]Xv\v Zrt£]w `pPbpw (base) ZrKvPym IÀ®hpamb {XntImWs¯ B{ibn¨t¸mÄ Bcy`S³ Hcp \qäm−v ap¼v ZrKvPym IÀ®am¡n Zr¤XnPym2 = ZrKvPym2 þ ZrKvt£]2 F¶ kq{Xw \ÂInbncp¶p. I\ymIpamcnbn kap{ZN{Ihmfw Ahew_ambn \S¯nb {KlW \nco£Ww Bcy`Ssâ kq{X§fn {]Xn^en¡p¶psh¶v ]dbmw. Sn {KlW¯nsâ Fkvs]\mIv \ÂIp¶ OmbbpsS hogvN Xmsg \ÂIp¶ Nn{X¯n ImWmw.
30
(M){Kla[ya§fpsS A¼c¸n¡p¶ kq£vaXbmWv Bcy`Sob¯nsâ asämcp khntijX. C´ybnse CXc tPymXnximkv{X·mÀt¡m, bh\Àt¡m AeIvkm{−nbbnse hnZzm·mÀt¡m, ssSt¡m {_mtlbpsS (AD1500) Imew hsc BÀ¡pw Xs¶ km²yamImXncp¶ kq£vaXbmWv Bcy`Sob¯n ImWp¶sX¶v sU¶nkv Uyq¡v F¶ tPymXnximkv{XÚ³ hnkvabn¡p ¶p. AXnkq£vaamb B[p\nIKWnXw sIm−pam{XamWv Cu kq£vaX shfnhmIp¶Xv. Cu Akm[mcW kq£vaX¡v ImcWsa´mWv? {Kl\nco £W§fmsW¦n AhbpsS kz`mhsa´v? Cu tNmZy¯n\p¯cw Bcy`Sobw tKmf]mZw tÇmIw 48 \ÂIp¶p. £nXnchntbmKmXv Zn\IrXv choµptbmKmXv {]km[nXtݵpx iinXmcm{KltbmKmXv XssYh Xmcm{Klmx kÀtÆ kqcysâ KWnXw `qanbpambpÅ kwKa¯n \n¶pw AYhm hnjpkw{Ia tam, £nXnPw AYhm N{Ihmf¯nse DZbmkvXab§Ä Bkv]Zamtbm kq£vaam¡p¶p. N{µsâ Imcy¯n AYhm Aamhmkn, kqcybpXn ASn Øm\ambpw {Kl§fpsS KWnXw {KlþN{µtbmK§fmepw km²yamIp¶p. Cu tÇmIw ZiKoXnIbnsebpw BcymjvSiXKoX§fpsSbpw ASnØm\am b BImi\nco£W§fpsS kw£n]vXhnhcWamWv. Cuhn[ \nco£W §Ä Bcy`S\m GXv Ime¯v \S¯s¸«p? KXIen 3620 se kqcy{Kl Ww N{µXpwKþ]mX§fpsS thKX, {`aWkwJy apXembh \nÝbn¡p¶Xn  Bcy`S\v hgn Im«nbmbncp¶psh¶v apIfn kqNn¸n¡pIbp−mbn. apIfn ]dª \nco£W]T\§fpsS km[pXsbbpw, Bcy`S³ Hcp kqcy{KlWw ImWp¶Xn\mbn ISen t]mbn F¶ sFXnlys¯bpw ]ecpw tNmZyw sNbvtX¡mw. Hcp heb{KlWw ImWp¶Xn\mbn ISen t]mbn {`jvS\mIphm³ Bcy`S³ X¿mdmInà þ F¶v hmZn¡p¶hcp−mImw. Bcy`Sob¯n\v ASnØm\amb \nco£W§Ä (KXIen 3619 sâ Ahkm \¯nepw KXIen 3620 epw, AD 519) tIcf¯n\pw N{a-h-«-¯n\pw {]tXyI {]kàn \ÂIp¶hbmsW¶v shfnhm¡p¶XmWv 15 s^{_phcn AD 519 \v Zriyamb ]qÀ®kqcy{KlWw. Cu ]qÀ®{KlWw \nco£n¨v \nÀ®bn¡ s¸« KWntXm]m[nIfpsS ]co£W¯n\v Nn§amk¯nse {KlWw \nco£n¡pI A\nhmcyambncp¶Xn\memWv Bcy`S³ s]m¶m\n¡v sX¡v ]Snªmdv ISen {KlW\nco£W¯n\v Hcps¼«Xv.
6. Bcy-`-S³ I\ym-Ip-am-cn-bnÂ...? KXIen 3620 se CXc {KlØm\KXnIfpsS kz`mhsa´mWv? AhbpsS \nco£Ww GXphn[amWv \nÀÆln¨ncn¡pI? BKÌv ]Xns\m¶mw XobXnbnse kqcy{KlW¯n\v ap¼pw ]n¼pw D−mb N{µ{KlW§fpw Cu Imebfhnse {KlØm\KXnIfpw ]cntim[n¨m Ing¡v ISense N{Ihmfw Ahew_ambn _p[þKpcpþip{I·mcpsS DZbhpw N{µbpXnbneqsS IrXyamb Øm\\nÀ®bhpw km[yambncp¶psh¶v a\Ênem¡mw. IpPþ i\nIfpsS Imcy¯n bmtaym¯ckw{Iahpw (Meridian Transit) Zriyambncp
31
¶p. {KtlmZbmkvXab§Ä kqtcymZbmkvXab§fpambn X«n¨p t\m¡n AhbpsS Øm\\nÀ®bhpw km²yambncp¶p. {Klw chn N{µ³ IpP³ _p[³ Kpcp ip{I³ i\n cmlp NþXpwKw
{KlWZn\a[ymÓ¯nse {KlØnXn tcJmwiw A£mwiw {Klwþchn DZbw 139°05'45" 139°04'15" 289°09'02" 124°20'50" 98°24'27" 103°18'10" 289°58'49" 137050' 146021'
--00°07' -06°11' 01°08' 00°07' -00°31' -00°35' ---
-0.025 150.05 -14.75 -40.69 -35.79 150.88 ≈ 20 ≈ 70
05:44 05:35 16:24 04:42 02:51 03:11 16:19
AkvXw 18:18 18:24 03:43 17:24 15:35 15:55 03:47
Cu {KlØnXnbn \n¶pw ]qÀ®þ{KlW kab¯v Hcp ]s£ Kpcpþ_p[ þip{I·mÀ Zriycmbn `hn¨ncn¡mw F¶v IcpXmw. he-b-{K-lW - -¯n km[yX Ipd-hm-sW-¶Xv {i²n-¡-Ww. i\nbpw IpP\pw cm{Xnbnepw Kpcpþ_p[þip{I·mÀ cmhnse Ing¡³ N{Ihmf¯nepw Zriyambncn¡bm \h{Kl§fpsSbpw N{µXpwK¯nsâbpw Øm\w Cu Znhkw hyàambncp ¶p. {KlW¯n\v kao]hÀ¯nbmb Imew t\m¡nbm I\ymIpamcn {Kl KWnX¯n\v Gähpw A\ptbmPyamb \nco£Ww km²yam¡nsb¶v a\Ênem¡mw. DZbmkvXabN{I-hmf§Ä I\ymIpamcnbn Zriyambncp¶p. {]Imiw ]c¡p¶Xn\v ap¼v I\ymIpamcnbn Kpcpþip{I·mcpsS DZbhpw i\nþIpP·mcpsS AkvXabhpw Zriyambncp¶p. kqcymt]£nIamb Cu hn[ \nco£W§fn \n¶v Gähpw IrXyamb Øm\\nÀ®bpw km²yamIp ambncp¶psh¶XmWv Bcy`Sob¯nse kq£vaX¡v \nZm\w. kqcyt\mSv ]qÀ®tam AÀ²tam Bb {`aW§Ä ]qÀ¯nbm¡phm³ {Kl§Ä¡mhiy amb Imew apIfn ]dª Kpþipþ_p DZbw, aþIp AkvXabw Chbn \n¶v km²yambncp¶p. {]Xn`mkw N{µ{KlWw N – ip N – Kp N – _p N –c N – Ip N –a n N{µ{KlWw
XobXn 27 Pqsse 8 Aug 519 AD 8 Aug 519 AD 10 Aug 519 AD 11 Aug 519 AD 23 Aug 519 AD 23 Aug 519 AD 26 August
(Perigee close)
cmhnse Ing¡v cmhnse Ing¡v cmhnse Ing¡v kqcy{KlWw cm{Xn, Xe¡v aosX cm{Xn, Xe¡v aosX Also perigee
32
kqcy{KlW¯nt\mSSp¯v KXIen 3620  Bcy`Sob¯nsâ kq£vaX¡v hniZoIcWw \ÂIp¶ FÃm {Kl{]Xn`mk§fpw I\ymIpamcnbn Zriyam bncp¶psh¶v CXn\m a\Ênem¡mw. Ipw`wþNn§w amk§fnse Cu kqcy{KlW§Ä a[ymÓt¯mSSp¯mbncp ¶Xn\m ew_\w Ipdhpw {KlW§fpsS ]qÀ®Imew kv^pS]ÀÆm´ t¯mSSp¯pw Bbncp¶p. Cu hkvXpX Bcy`Sob¯n \ap¡v \ngen¨v ImWmw. kv^pSiinamkmt´ƒÀt¡ ]mXmkt¶m bZm {]hniXoµpx `qÑmbmw ]£mt´ XZm[ntIm\w {KlWa[yw (tKmfwþ36) kv^pSmamhmky´y¯n (kqcykv^pSw = N{µkv^pSw) ]mXk¶n[nbn (cmlptIXp¡fnsem¶nt\mSSp¯v) N{µ³ kqcyt\mSv tbmKw sN¿pt¼mÄ kqcy{KlWhpw ]uÀWanN{µ³ `qOmbbn {]thin¡pt¼mÄ N{µ{Kl Whpw kw`hn¡p¶p. ]£m´w AYhm ]ÀÆm´w Gsd¡psd {KlWa[y ImeamWv. ]£m´w AYhm ]ÀÆm´w Gsd¡psd {KlWa[yImeamWv þ F¶ {]kvXmhw kqcy{KlW¯n\v icnbmIpI ew_\w Ipdhmb a[ymÓ{KlW §fn am{XamWv. apIfn Bcy`S\m \nco£n¡s¸«Xmbn ]dbs¸« c−v kqcy{KlW§fnepw Cu ØnXn ImWp¶Xn\m Sn \nco£W§Ä tÇmI¯nse {]amWw cq]oIcn¡p¶Xn Bcy`S\v t{]cIambncp¶psh¶v a\Ênem¡mw. Bcy`Sobw `mcXob tPymXnximkv{X¯n Hcp \hbpK¯nsâ XpS¡ ambncp¶psh¶ A\pam\¯n\v `mcX¸pgbpsS Icbnepw (]X\Øew) I\ymIpamcnbnepw Ien 3620  Zriyamb JtKmfob {]Xn`mk§fpw Ah¡v Bcy`Sob¯n ZriyamIp¶ {]Xn^e\hpw km[pX \ÂIp¶p.
Xmc]RvPc¯nsâ, kqcysâ `qanbpsS kzbw {`aWw.
Bt]£nI
{`aWw
þ
{]mtWss\Xn Iemw `qx þ `qan Hcp {]mW\n Hcp Ie Xncnbp¶p þ Bcy `Ssâ Cu hm¡pIsf hcmlanlnc\pw, eÃmNmcy\pw, {_ÒKp]vX\pw \ninXamb ]cnlmkt¯msS hnaÀin¡pIbp−mbn. kqtcymZb¯n IqSp hnSp¶ ]dhIÄ `qan Id§p¶psh¦n sshIn«v F§s\bmWv Iq«n Xncn s¨¯pI? F¶ tNmZyw {_ÒKp]vX\pw eÃmNmcy\pw DbÀ¯pIbp−mbn. A\ptemaKXnÀ\uØx ]iyXyNew hntemaKw bZzXv ANem\n `m\n XZzXv ka]ÝnaKm\n e¦mbmw (tKmfwþ9) DZbmkvXab \nan¯w \nXyw {]htlW hmbp\m £n]vXx e¦mka]ÝnatKm `]RvPcx k{Ktlm {`aXn (tKmfwþ10)
33
\uIbn k©cn¡pt¼mÄ Xoc¯pÅ Ip¶pIÄ ]nt¶m¡w ]mbp¶Xp t]mse Ne\anÃm¯ \£{X§Ä e¦bn Ing¡pZn¨v ]Snªmtdm«v Id§p ¶Xmbn tXm¶p¶p. AXpt]mse DZbmkvXab§Ä¡v ImcWw `]RvPcw {]hlhmbphn\m ]Snªmtdm«v Id¡s¸Sp¶Xn\memsW¶v \nXyhpw A\p`hs¸Sp¶p. Gähpw imkv{Xobamb Cu A\p`h{]kvXmhs¯, imkv{XNn´sb ]n¶oSv h¶ {]Xn`IÄ \ncmIcn¨sX´v? Bcy`Ssâ X\Xmb Cu {]kvXmh¯n\v ]n¶nse A\p`hsa´mWv? IStemcw ]än \uIbn bm{XsN¿p¶bmfnsâ A\p`hamWnXv. ]IemsW ¦n kqcy³ bm{XnIs\ A\p[mh\w sN¿pt¼mÄ sam«¡p¶pIfpw aäpw ]ndtIm«v amdp¶Xmbn tXm¶p¶p. cm{XnbnemsW¦ntem, N{µ\pw \£{X§ fpw bm{XnIs\ ]n´pScp¶Xmbn tXm¶pt¼mÄ Xoc¯pÅ AYhm k© cn¡m¯ \uIIfnse hnf¡pIÄ ]nt¶m«v k©cn¡p¶Xmbn tXm¶pw. Cu A\p`hhpw I\ymIpamcnbn PecminbpsS Ing¡pw ]Snªmdpambn Zriyamb XmcmKW§fpsSbpw kqcyN{µmZnIfpsSbpw DZbmkvXab§fmWv Pecminsb DÄs¡mÅp¶ `qan Id§p¶p F¶ t_m²yw Bcy`S\p \ÂInbXv. Nn{Xw t\m¡pI. Ing¡³ N{Ihmf¯n Kpcpþip{I·mÀ DZn¡p t¼mÄ ]Snªmd³ N{Ihmf¯n IpP\pw i\nbpw AkvXan¡p¶Xv I\ymIpamcnbn ISen\p IpdpsI Zriyambncp¶p. PecminbpsS, PetKmtfm]cnXe¯n\v Ing¡pw ]Snªmdpw Cu c−p hnf¡pIÄ sImfp¯nsh¨ t]mse AYhm ^Â{Iw t]mse Ah Xncnbp¶Xmbn Bcy`S\v A\p`hw \ÂInb Cu Zriyw Xs¶ `qanbmWv Id§p¶Xv F¶ t_m²yw \ÂInbncn¡Ww. amaqepIsf `b¡msX hn¹hmßIambn `qan Id§p¶psh¶v Bcy`Ss\ ]Tn¸n¨Xv almKpcp¡·mcmb {Kl§Ä,Kpcp, ip{I³, i\n. IpP³ ChÀ Xs¶bmWv. A¡m-e¯v imkv{X-Im-c-·m-cpsS CSbn Xs¶ \ne-\n-¶n-cp¶ Aim-kv{Xo-b-X¡v hyà-amb km£yw btim-[-\cmb tPymXnx-im-kv{X-Ú-cmb {_Ò-Kp-]vX\pw -e-Ãm-Nmcycpw \ÂIp-¶p-−v. "(B-cy-`-S³ ]d-bp-¶-Xp-t]m-se) `qan Id§p-¶p-sh-¦nÂ, {]`m-X-¯n IqSp-hn«v ]d-¡p¶ ]d-h-IÄ sshIp-t¼mÄ Iq«n Xncn-s¨-¯p-¶-sX-§s\?" F¶ bpàn-sIm−v \nin-X-ambn hnaÀin¨v `qan Id-§p-¶n-söv kaq-ls¯ t_m²y-s¸-Sp-¯nb imkv{X-Ú-·m-cpsS Ime¯n\v t]mepw ap¼mWv hnkvabn-¡p¶ kq£va-Xbpambn Bcy-`-S³ {]Xy-£-am-b-Xv. ]©-`q-X-§-fn-epÄs¸« BIm-is¯ Hgn-hm¡n Aán, Pew, hmbp, `qan Ch am{Xsa Bcy-`-S³ `qanbpsS `mK-ambn AwKo-I-cn-¡p-¶p-Åp (tKmfwþ6). 11 BKÌv 519 AD `mcXob tPymXnximkv{X¯nse Gähpw \nÀ®mbI amb
\nco£W§fpsS Znhkambncp¶psh¶v ]d-bmw. N{a-h-«hpw a−-¡m-Spw, tIcf¯nse c−v Znhy-k-¶n-[n-IÄ KX-Ien -3619-3620 Ime¯v Ipw`w-þ-Nn§w amk-§-fn A²ym-ßn-I-]-cn-th-j-amÀ¶ JtKm-fob {]Xn-`m-k-§Ä¡v thZn-bmbn-¯o-cp-Ibpw Ah-bpsS \nco-£-W-§Ä `mc-X-¯n KWn-X-þ-tPym-Xnx-imkv{X-cwK¯v Hcp \qX-\-im-kv{X-]m-c-¼-cy-¯n\v Imc-W-am-Ip-Ibpw sNbvXp.
34
7. AKkvtXymZbw þ Bcy`Ssâ {]amWw sXtäm? Bcy`Ssâ AKkvtXymZb {]amWw BcymÀ[cm{Xkn²m´¯n \n¶pw hcmlanlnc{]`rXnIÄ D²cn¨v ]n¡me¯v e`yamb {]amWamWv. ]qÀÆJWvUJmZyI¯nse Bdma[ymb¯n {_ÒKp]vX³ D²cn¨ncp¶ Xmsg \ÂIp¶ {]amWw H³]Xmw \qäm−n `t«mXv]e³ sXämsW¶ Btcm]Wt¯msS sh«n¡fbpIbp−mbn. cminNXpjvtIW bZm kzm£mwibptX\ `hXn XpteymƒÀss¡x DZtbmƒKkvXyky XZm N{ImÀ[mtÑmZntXƒkvXabx kqcy³ \mepcminbpw A£mwihpw IqSnb `mKbnse¯pt¼mÄ AKkvXy³ DZn¡pIbpw N{ImÀ[w AYhm Bdpcminbn \n¶v ap³]dª \mep cminbpw A£mwihpw Ipd¨p In«p¶ Øm\¯v (c−v cminþA£mwiw) kqcys\¯pt¼mÄ AKkvXy³ AkvXan¡pIbpw sN¿p¶p. AXmbXv, A£mwiw φ BIpt¼mÄ AKkvXy\£{X¯n\v (Canopus)þ AKkvtXymZbkqcy³ λs = 1200 + φ AKkvXymkvXabkqcy³ λs = 600 þ φ eÃmNmcy\pw Cu {]amWw D²cn¡p¶psh¦nepw km[pXsb¸än At±lw Xr]vX\mbncp¶nsöv Bcy`SinjyÀ C§s\bpw ]dbp¶p F¶ ]cmaÀi ¯n \n¶pw a\Ênem¡mw. aÃnImÀÖp\kqcnbpsS injy[ohr²nZw hymJym\¯n \n¶pw Cu hkvXpX hyàamIp¶p.
{]amW¯nsâ km[pX Cu {]amW¯nsâ km[pX ]cntim[n¡phm³ hnhn[ Øe§fnse AYhm A£mwi§fnse AKkvXysâ kqtcymZbmkvXabIme§fnse D¶Xmwi s¯ (Altitude) kqcykv^pShpambn _Ôs¸Sp¯n t\m¡nbm aXn. \ap¡nhnsS N{a-h«w (10N51) DÖbn\o (24N00) F¶o Øe§Ä Z£nW þD¯c `mcXs¯ {]Xn\n[oIcn¨v DZmlcW¯n\mbn ]cnKWn¡mw. AKkvXysâ AkvXabw λs = 600 þ φ Bcy`Ssâ Imeamb KXIen 3620 ]cnKWn¡pt¼mÄ kqcykv^pSw 25-600 BIpt¼mÄ kqcymkvXabIme¯v AKkvXysâ D¶Xmwiw Nn{Xwþ1 \ÂInbncn¡p¶p. DÖbn\n¡v λs = 60 - φ = 36 BIpt¼mÄ AKkvXy\v D¶Xmwiw Ggv Un{Kn am{XamWv. ZriyamIp¶Xn\v th− D¶Xmwiw 12-14 Un{Kn BIbm kqcysâ 36 XobXn (25G{]n 519AD ) AKkvXysâ kqtcym]cnZriyXbpsS Ahkm\XobXn AYhm AKkvXy AkvXab ImeaÃ. {]amWw AXn\m DÖbn\n¡pw D¯c`mcX¯n\pw AkvXabw kw_Ôn¨v icnbÃ. N{a-h«w 10N51 \v λs = 60-10.85 = 49 BIpt¼mÄ AKkvXy\v D¶Xmwiw 14 Un{KnbmIp¶p. AXn\m kqcysâ Cu
35
XobXn¡v N{a-h-«¯v kqcymkvXab¯n\v tijw AKkvXys\ Ahkm\am bn ImWmhp¶XmWv. Nn{Xwþ1 Cu hkvXpXIÄ hyàam¡p¶p. Agastya sets - Rule of Aryabhata 20.0
10N51 18.0
Fig.1 60 - Latitude
Altitude of Agastya
16.0 14.0 12.0 10.0
24N
8.0
10N51-Agastya sets 6.0
24N00-Agastya sets 4.0
Poly. (10N51-Agastya sets)
2.0
Poly. (24N00-Agastya sets)
0.0 25.0
30.0
35.0
40.0
45.0
50.0
55.0
60.0
Sun's Longitude
AKkvtXymZbw λs = 120 + φ DÖbn\n¡v λs = 120 + 24 = 144 BIpt¼mÄ kqtcymZbIme¯n AKkvXysâ D¶Xmwiw A©v Un{KnbmWv. DZb¯n\v ap¼mbn C¡mcW¯m AKkvXy³ ZriyamIbnÃ. F¶m N{a-h-«¯v λs = 120+10.85 = 131 AXmbXv kqcysâ XobXn 131 BIpt¼mÄ, DZbIme¯n AKkvXy\v D¶Xmwiw 12 Un{KnbmWv. kqtcymZb¯n {]Imiw ]c¡pw ap¼v AKkvXy³ N{Ihmtfm]cn ZriyamsW¶v CXn\m a\Ênem¡mw.
AKkvXy³ AkvXabw
kqcyXobXn D¶Xmwiw = 0
ZriyIme kqcy³
hyXymkw
73.8
60−φ = 49
25
24N00
50.8
60−φ =36
15
DZbw 10N51
110.7
120+φ =131
20
DZbw 24N00
133.5
120+φ= 144
10.5
10N51
AkvXabw
36
Nn{Xwþ2 AKkvtXymZbhpw kqcy\pw Rise of Agastya-Rule of Aryabhata 25.0
Fig.2 120 + Latitude Altitude of Agastya
20.0
10N51 15.0
24N 10.0
10N51 (Agastya rises) 24N00 (Agastya sets) 5.0
Poly. (24N00 (Agastya sets)) Poly. (10N51 (Agastya rises))
0.0 100.0
110.0
120.0
130.0
140.0
150.0
160.0
170.0
180.0
Sun's Longitude
Nn{X§fneqsS hyàam¡nb bpàn apIfn \ÂIp¶ ]«nIbn \n¶pw asämcphn[¯n a\Ênem¡mw. AKkvXysâ DZbmkvXab Ime§Ä¡v Bcy`Ssâ {]amWw \ÂIp¶ kqcyXobXn þ (I) AKkvXy AkvXab¯nsâ kqcyXobXn N{a-h-«s¯ D¶Xmwiw iq\yamIp¶ XobXn¡v 25 Znhkw ap¼mWv. AXn\m Cu kqcyXobXn¡v AKkvXy³ AkvXabtijw IjvSn¨v ZriyamIp¶p. (J) AKkvXy AkvXab¯nsâ kqcyXobXn DÖbn\nbn D¶Xmwiw iq\yamIp¶ XobXn¡v 15 Znhkw am{Xw ap¼mWv. AXmbXv IqSpX Znhk§fpsS hyXymkw th−nbncp¶ Øe¯v hyXymkw IpdhmWv. AXn\m Cu kqcyXobXn¡v ap¼v Xs¶ AKkvXys\ AkvXabtijw ImWmXmIp¶p AYhm AKkvXysâ AkvXabw ]¯v XobXnsb¦nepw ap¼v \S¡p¶p. (K) AKkvtXymZb¯nsâ Imcy¯nepw kam\amWv ØnXn. s]m¶m\nbn 20Znhkw hyXymkw DÅt¸mÄ DÖbn\nbn 15 am{XamWv hyXymkw. Bcy`Ssâ AKkvtXymZbmkvXab {]amWw N{a-h-«s¯tbm AYhm kao] {]tZ-i-§-fm-bn-cp¶ {ih-W-_ÂtKmf(AivaIw)bnsetbm \nco£Ww ASn Øm\ambn cq]w \ÂIs¸«XmsW¶v CXn\m hyàamIp¶p. Bcy`Ssâ injyÀ ssIs¡m−ncp¶ {]amWw sXsä¶v iTn¨Xv Gähpw icnbmsW¶v kztZi sXfnhn\m Øm]nXamIpIbpw sN¿p¶p.
37
8. IÃp-cp-«p-IYbnse {XntIm-W-anXn þ ssk³ (`p-P-Pym) sImssk³ (tIm-Sn-Pym) D]-Úm-Xmhmb Bcy-`-S³ Bcy-`-Ssâ ss]Xr-I-t¯m-sSm¸w tIc-f-¯n\v \jvS-am-Ip-am-bn-cp¶ JymXnbmWv KWn-X-im-kv{X-¯nse {]kn-²hpw kÀ¤m-ß-I-hp-amb ImÂsh-bv]p-I-fnsem-¶mb ssk³, sImssk³ aqey-§Ä. tKmf-K-Wn-X-¯nsâ hgn-¯m-c-bn BZy-ambn bh-\cpsS RmWp-IÄ¡v ]Icw (Chords of Ptolemy) D¶-Xnbpw (R*sineθ) ]mZhpw (R*Coseθ) BZy-ambn D]-tbm-K-s¸-Sp-¯nb KWn-X-Ú³ Bcy-`-S-\m-Wv. Bcy-`-So-b-¯n e`y-amb \qX-\-k-t¦-Xs¯ CX-c-kn-²m-´-Imc-·mÀ A\p-I-cn-¨-Xn-\m C¶ e`y-amb `mc-Xo-btPymXnx-imkv{XIrXnI-fnseÃmw Xs¶ AÂ]w Nne hyXym-k-t¯msS Bcy-`-Ssâ R*sineθ aqey§Ä e`y-am-Wv. Fhn-sS-bmWv Cu \qX-\-co-Xn-bpsS DÛhsa¶ Imcy-¯n AXn\m k¶n-Kv²m-hØ \ne-\n¡p-¶p. Cu k¶n-Kv²m-h-Ø¡v ]cn-lm-chpw tIc-f-¯n-emWv Cu kt¦-X-¯nsâ ]nd-hn-sb¶ hkvXp-X¡v hyà-amb bpànbpw ChnsS \ÂIp-hm³ {ian-¡p-¶p. tIk-cn-_m-e-Ir-jvW-]n-Å-bpsS injy-\mb tae-§¯v \mcm-b-W³ Ip«n-bpsS kwL-Im-e-N-cn{Xw Xangv tcJ-Isf Bkv]-Z-ambn \mdm-W¯v {`m´³ lcn-Z¯-\m-sW¶ hkvXpX hyà-am-¡p-¶p-−v. s]m³ap-Sn-bmÀ F¶ {]kn-²-\m-bncp¶ \mdm-W¯v {`m´sâ Imew KX-Ien 3785 BIp-¶p (CE684)15. \mdmW¯v {`m´-tâ-Xmbn sFXn-ly-§-fn-eqsS Adn-b-s¸-Sp¶ hnIrXnbmb IÃp-cp«p-IY At±lw hnI-kn-¸n-s¨-Sp¯ Pymhv k{¼-Zm-b-¯nsâ {]Xo-Im-ßI BJym-\-am-sW¶v \mcm-b-W³ Ip«n kqNn-¸n-¡p-¶p. ]s£, Pymhv k{¼-Zmbw lcn-Z-¯\v ap¼v Bcy-`-So-b-¯nepw ]n¶o-Sp-−mb \nc-h[n kn²m-´-§-fnepw ImWp-¶-Xn-\m IÃp-cp-«p-IY Pym¡sf tIc-f-¯n Bcy-`-S³ hnI-kn-¸n-s¨Sp-¯-Xnsâ {]Xo-Im-ßI Ah-X-c-W-am-sW¶v A\p-am-\n-¡mw. IÃp-cp«pIYbn Bcy-`-Ssâ X¯z-{]-kvXmhw \ng-en-¡p-¶Xv Xmsg hyà-am-¡p-¶p. D¶-Xn-h-cp-¯p-hm-s\-{Xbpw ]cm-[o\w ]ns¶-b-§-t[m-K-Xn-s¡-{X-bp-sa-fp-¸amw F¶ {]kvXmh¯n `pP-Pymhpw tImSn-Pymhpw A´Àeo-\-am-Wv.
Pym¡Ä Bcy-`-So-b-¯n km[mc-W-amb Hcp hr¯w ]cn-K-Wn-¡p-t¼mÄ (Nn{Xw {i²n-¡p-I) AXnsâ hymkmÀ²-amb OA =R = OB, θ F¶ tImWns\ DÄs¡m-Åp-t¼mÄ, \ap¡v Xmsg \ÂIp¶ ka-hm-Iy-§Ä {XntIm-W-an-Xn-b-\p-k-cn¨v e`n-¡p-¶p. Sine θ = BF/OB = BF/R AYhm BF = R*Sine θ = D¶Xn. Cos θ = OF/OB AYhm OF = OB*Cosθ = R*Cos θ = ]mZw 15
K. Chandra Hari, Date of Haridatta, Promulgator of the Parahita System of Astronomy in Kerala, IJHS, September 2002, p.223-237. lcn-Z-¯sâ Imew kw_Ôn¨v \ne\n¶ FÃm Ahy-à-I-sfbpw tPymXnÀK-Wn-X-]-c-ambn Zqco-I-cn-¡p-¶-XmWv Cu ]T-\w.
38
ChnsS F F¶Xv A bn \n¶pw OB bnte-¡pÅ ew_--þ]mZ-am-Ip-¶p. tIm¬ ∠AOB = θ, ∠ AFO =900, F¶v Nn{X-¯n \n¶pw a\-Ên-em-¡mw. B Sine θ = BF/OB = BF/R AYhm BF = R*Sine θ = D¶Xn.
θ O
F
A
Cos θ = OF/OB AYhm OF = OB*Cos θ = R*Cos θ = ]mZw
∠θ {XntIm-W-an-Xn-bn 900 hsc-bm-Ip-t¼mÄ D¶Xn = hymkmÀ²w F¶v e`n¡p-¶p. Bcy-`-S³ 900 sb 24 ka-`m-K-§-fm¡n (3045' =225' x 24 =900) 24 `pP-Pym¡f \ÂIn-b-Xnsâ bpàn Nn{X-¯n \n¶pw a\-Ên-em-¡mw. BZy-Pymhv R*sine 3045' = 225' Xs¶ BIp¶p. Cu GIIw D]-tbm-K-s¸-Sp¯nbmWv R*sine 900 = R = 3438' hsc-bpÅ Pym¡Ä \ÂI-s¸-Sp-¶-Xv. θ IqSp-¶-X-\p-kcn¨v aqeyw \nÀ®-bn-¡pI D¯-tcm-¯cw {ia-I-c-am-Wv. Cu \nÀ®-b-¯n-\pÅ \nc-h[n coXn-Ifpw ka-hm-Iy-§fpw ]n¡me tPymXnx-im-kv{X-kn-²m-´-§fn e`y-am-Wv. AXm-bXv R*sine θ AYhm D¶Xn hcp-¯pI IÃp-cp«n Db-c¯n-se-¯n-¡p-¶Xv t]mse {ia-I-c-am-Wv. F¶m D¶Xn hcp-¯n-¡-gn-ªmÂ. `pP-Pym-¡Ä e`y-am-bm ]mZw AYhm R*cos θ \nÀ®bn¡pI R*cosθ = R*sin(90-θ) F¶ kq{X-ap-]-tbm-K-s¸-Sp¯n, AXm-bXv ]«nI Xncn¨v hmbn¨v \njv{]-bmkw km[n-¡m-hp-¶-Xm-Wv. KWn-X-Út\m A²ym-]-It\m AÃm-¯-Xn-\m Cu hni-Zo-I-c-W-¯n-epÅ ]Zm-h-en-bpsS ¢njvSX kZbw £an-¡p-I. IÃp-cp-«p-I-Y-bn A´Àeo-\-amb D¶XnbpsSbpw ]mZ-¯n-sâbpw bpàn Bcy-`-So-b-¯nse Pym¡-fpsS {]Xo-ImßI Ah-X-c-W-am-Wv.
]T-\-¯nse {][m\ \nKa\§Ä \½psS tIc-fs¯ kw_-Ôn-¨n-S-t¯mfw \jvS-{]m-b-am-bn-¯oÀ¶n-cp¶ Bcy-`S-sâ ss]XrIw Cu ]T-\-¯n-eqsS Xncn¨p ]nSn-¡m³ Ign-bp-¶p-sh-¶-XmWv Cu ]T-\s¯ khn-ti-j-am-¡p¶ hkvXp-X. IqSm-sX, Bcy-`-Ssâ \yq\-X-Ifmbn hnaÀin-¡-s¸-«n-cp¶ bpàn-I-sfÃmw Xs¶ JtKm-fob \nco-£Ww ASnØm-\-amb Is−-¯-ep-I-fm-sW¶v ChnsS hyà-am-¡p-I-bp-−m-bn. Bcy-`Ssâ Gähpw {]Jym-X-hn-aÀi-I-\mb {_Ò-Kp-]vXs\ \nco-£Ww \S-¯m¯ KWn-X-hn-{In-b-¡m-c-s\¶v htS-iz-c³ hnti-jn-¸n-¨Xv ChnsS kvac-Wo-b-am-Wv.
39
aXn-bmb ]T-\-\n-co-£-W-§Ä \S-¯m-Xn-cp¶hcpw Aim-kv{Xo-bX ]peÀ¯nbn-cp-¶-h-cp-amWv Bcy-`-Ssâ hnaÀi-I-cm-bn-cp-¶-sX¶v Cu ]T-\-¯n-eqsS hyà-am-Ip-¶p. Bcy-`-Ssâ A\ym-Zr-i-amb JymXn-sb-´p-sIm-−m-sW¶ tUm. Pn. Xnt_m-«nsâ tNmZy-¯n\v Xr]vXn-I-c-amb kam-[m-\hpw ChnsS e`y-am-Wv. Cu ]T\¯n \n¶pw Dcp¯ncnbp¶ {][m\ hkvXpXIsf A¡-an«p ]dªm þ 1.
Bcy-`-Ssâ kztZiw kw_-Ôn¨v \ne-hn-en-cp¶ Ahy-à-IÄ¡v Xr]vXn-Ic-amb kam-[m-\hpw Aiva-Io-b³, Aiva-Io-b-X-{´w apX-embn tPymXnx-imkv{X-]m-c-¼-cy-¯n Bcy-`-S\v kn²-am-bn-cp¶ hnti-j-W-§Ä¡v aXnbmb hni-Zo-I-c-Whpw ChnsS NÀ¨ sN¿-s¸-«p.
2.
Bcy`Sob¯nse Ime-{In-bm, tKmfw F¶o ]mZ-§-fnse KoX-§f - n-e´Àeo-\-amb hnhn[ kqN\If\pkcn¨v Bcy`Ssâ kztZiw AYhm \nco£WØm\w s]m¶m\n¡Sp-¯pÅ N{ah«w (10N51, 75E45) taJe bmIp¶p.
3.
N{ah«w Aiva-I-P-\-]-Z-¯nsâ `mK-am-bn-cp-¶p. Aiva-I-sa¶ ssP\tI{µw C¶s¯ {ih-W-_ÂtKmfsb tI{µo-I-cn¨v ]pcm-X-\-Im-e¯v \ne-\n¶ ssP\-P-\-]-Z-am-sW¶v ]n¡m-e¯v {]Xn-a-I-fm-¡-s¸« {ih-W-_ÂtKm-fbnse sImSpw-I-Ãp-IÄ (Stone Monliths) kqNn-¸n-¡p-¶p. Cu \nK-a-\-¯n\v Dt]m-Zv_-e-I-amWv N{ah«¯v imkvXmhnsâ km¶n-²yw. ssP\þ_u² ]mc¼cy¯n \nehnÂh¶ Bcm[\maqÀ¯nbmWv imkvXm-hm-sW¶ Ncn-{X-Im-c-·m-cp-sS Is−-¯-ep-Ifpw N{a-h-«¯v ASp-¯-Im-e¯v e`y-amb ]pcm-h-kvXp- kw_-Ô-amb sX-fn-hp-Ifpw ChnsS kvac-Wo-b-am-Wv.
4.
Bcy`Sob¯nse bpKLS\bpsS ssP\kz`mhhpw, {ipXn-þ-kvarXn hncp²-ambn (th-tZ-Xn-lm-k-]p-cm-W-§Ä) \ÂIn-bn-cn-¡p¶ IrXm-Zn-bp-KssZÀLy-§fpw sshZn-I-]mc¼cy-¯n \n¶pw hyXy-kvX-amb kmwkvImcnI kml-N-cy-¯n-emWv Bcy-`-Ssâ {]Xn` {]^p-Ã-am-b-sX¶v kqN\ \ÂIp-¶p.
5.
`q]cn[nþkv]jvS`q]cn[n_Ôhpw Bcy`Ssâ tacp]cn[n \ÂIp¶ bpànbpw kzX{´amb `q]cn[n aqey§Ä \ÂInb tPymXnximkv{XÚ ·mcpsSsbÃmw kztZiw \nÀ®bn¡p¶Xn\v klmbIamWv. Cu ASnØm-\-¯n kzIo-b-ambn kn²m-´-§Ä Ah-X-cn-¸n¨ FÃm tPymXnx-imkv{X-Ú-·m-cp-sSbpw Ah-ew-_-am-bn-cp¶ tZi-¯nsâ A£mwiw Is−¯mw. e¦-þ-D-Ö-bn\o bmtaym-¯-c-þ-tc-Jm-kv]-Z-amb tZim-´-c-¯n \n¶v tcJmw-ihpw \nÀ®-bn¨v Øew IrXy-ambn \nÀ®-bn-¡m-hp-¶-Xm-Wv.
6.
Bcy`Sob¯nsâ cN\mImew KXIen 3620 BsW¶v N{ah«¯pw Z£nWtIcf¯nepw A¡me¯v Zriyamb ]qÀ®kqcy{KlW§Ä kqNn¸n¡p¶p. kqcyþss]Xmalkn²m´§fnse Øqeamb KWnX s¯ Bcy`S³ \nco£Wþ]co£W§fneqsS ]cnjvIcn¨v kq£va am¡nbXmbn Bcy`Sobkn²hpw B[p\nIKWnX]chpamb kv^pSþ a[ya§fpsS XmcXay¯n \n¶pw a\Ênem¡mw.
40
7.
Bcy`Ssâ sXäpIfmbn {_ÒKp]Xv³ hnaÀin¨ \yq\XIsfÃmw Xs¶ kztZi¯v \S¯nb \nco£W§fneqsS F¯nt¨À¶ imkv{Xob \nKa\§fmsW¶v ChnsS hyàam¡s¸SpIbp−mbn.
8.
anlncmZnIfm D²cn¡s¸«psh¦nepw km[pX kwibn¡s¸SpIbpw `t«mXv]e\m XnckvIcn¡s¸SpIbpw sNbvX Bcy`Ssâ AKkvtXym ZbmkvXab {]amWw kztZiamb N{ah«¯n\v Gähpw kq£vaamsW¶v B[p\nIKWnXcoXnbneqsS hyàamIp¶p.
9.
Bcy`Sob¯nse hnhn[ bpànIÄ¡v ImcWamb {]Xn`mk§Ä ]eXpw þ AÀ¡m{Kw, NcJWvUw, DÖbn\o A£mwiw (22N30) IS bm{Xbpw {KlW\nco£Whpw, I\ymIpamcnbnse Nn§amk \nco£W §fpw `qanbpsS {`aWw kw_Ôn¨ \nKa\hpw, N{µXpwKw, ]mXw ChbpsS {`aWkwJyIfpsS ]cnjvIcWw þ ]T\¯n CZw {]Yaambn hyàam¡s¸Sp¶p. tacp]cn[n, {KlWa[yImew Ch kw_Ôn¨ {]amW§Ä¡v Bcy`Ssâ ho£Ww imkv{Xobambncp¶psh¶pw ]T\w hyàam¡p¶p.
10. \mdm-W-¯p-{`m-´sâ IÃpcp«p-I-Y-bpsS s]mcpÄ Bcy-`-S³ tIc-f-¯nÂ
cq]w \ÂInb Pymþ-K-Wn-X-¯nsâ {]Xo-Im-ß-I-hn-h-c-W-am-sW¶v hyàam-Ip-¶p. ssk\pw sImssk\pw tIc-f-¯nsâ ss]Xr-I-am-sW¶v Cu hkvXpX sXfnhv \ÂIp-¶p. 11. s]m¶m\n¡v Ad_nIfpambp−mbncp¶ I¨hS_Ôw AeIvkm{−nb
bpambn tIcfs¯ _Ôn¸n¡pIbpw AXn]pcmX\ambn _m_ntemWn epw {Koknepw \ne\n¶ tPymXnximkv{XhnÚm\w A§s\ tIcf¯n se¯pIbpw sNbvXXv `mcX¯n tPymXnximkv{X¯n\v Hcp \hbpKw Ipdn¡phm³ Bcy`Ss\ klmbn¨ncn¡Ww.
12. tIc-f-¯nsâ kmwkvIm-cn-I-]m-c-¼cy¯n\v sshZn-tI-X-c-amb ssP\-_u-² -
k-{¼-Zm-b-§-fn \n¶pw Imcy-amb kw`m-h-\-IÄ e`n-¨n-«p-s−¶v Bcy-`-Ss\-¸-än-bpÅ Cu ]pXnb shfn-s¸-Sp-¯-ep-IÄ kqNn-¸n-¡p-¶p. tIc-fo-b-Ncn-{X-s¯-¸än IqSp-X hkvXp-\n-jvT-amb ho£-W-§Ä¡v Cu ]T\w t{]c-I-am-Ip-sa¶v {]Xym-in-¡p-¶p. 13. `c-XmXv þ `mc-XmXv hmb-\-bnepw (]m-Tw) hymJym-\-¯nepw D−m-Ip¶
hyXym-k-§Ä NÀ¨ sN¿-s¸-«-X-\p-k-cn¨v Bcy-`-So-bhpw sFtlmÄ enJnXhpw `mc-X-bp²w ]cm-aÀin-¡p-¶n-Ã. Ej-`-tZ-hsâ aI\pw ssP\cpsS BZy-temI-N-{I-hÀ¯n-bpamb `c-X-\mWv Bcy-`-So-b-¯nse KoXn-I-bnepw sFtlmÄ enJn-X-¯nepw ]cm-aÀin-¡-s¸-Sp-¶-Xv. `mc-X-bp²w Ien-bp-Km-Zn(3102BC)bn-em-sW¶ hmZs¯ ]qÀ®-ambpw XÅn-¡-f-bm³ Cu sXfnhv ]cym-]vX-am-Wv. 14. N{ah«w imkv{X-þ-km-ln-Xy-cw-K§fnse AXoh {]Xn-`m-[-\-cmb, c−v hyXykvX hyàn-I-fpsS, Bcy-`-S³ (CE 522), Xp©s¯-gp-¯-ѳ (CE1522) Pohn-X-¯m [\y-amb ]pWy-`q-an-bm-Wv. tIcfw P·w \ÂInb
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Cu alm-]p-cp-j-·m-cpsS tXtPm-hn-emkw IpSn-sIm-Åp¶ N{a-h-«-¯-¸sâ k¶n-[nsb ]pcm-h-kvXp-h-Ip¸v th−-hn[w Im¯p-kq-£n-t¡-−-Xm-Wv. 15. kqcy-N-{µ-am-cpÅ Ime-t¯mfw Bcy-`-Ssâ JymXn \ne-\n¡p-sa-¶-XnÂ
kwi-b-an-Ã. imkv{X-temI¯n\m-sI-¯s¶ N{a-h«w A\-Xn-hn-Zq-c-`m-hnbn ]pWy-XoÀ°ambn `hn-¡s« F¶ {]mÀ°-\-tbmsS, Hmw lcnx {ioKW]Xsb \ax sI. N{µlcnx chandra_hari18@yahoo.com 8/9/2007 4:08 AM
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