{"id":93004,"date":"2025-09-30T03:00:49","date_gmt":"2025-09-29T21:00:49","guid":{"rendered":"https:\/\/sarakhon.com\/?p=93004"},"modified":"2025-09-29T18:37:21","modified_gmt":"2025-09-29T12:37:21","slug":"%e0%a6%aa%e0%a7%8d%e0%a6%b0%e0%a6%be%e0%a6%9a%e0%a7%80%e0%a6%a8-%e0%a6%ad%e0%a6%be%e0%a6%b0%e0%a6%a4%e0%a7%87-%e0%a6%97%e0%a6%a3%e0%a6%bf%e0%a6%a4%e0%a6%9a%e0%a6%b0%e0%a7%8d%e0%a6%9a%e0%a6%be-290","status":"publish","type":"post","link":"https:\/\/sarakhon.com\/?p=93004","title":{"rendered":"\u09aa\u09cd\u09b0\u09be\u099a\u09c0\u09a8 \u09ad\u09be\u09b0\u09a4\u09c7 \u0997\u09a3\u09bf\u09a4\u099a\u09b0\u09cd\u099a\u09be (\u09aa\u09b0\u09cd\u09ac-\u09e8\u09ef\u09ea)"},"content":{"rendered":"<p style=\"text-align: center;\"><strong>\u09ad\u09be\u09b0\u09a4\u09c0\u09df \u098f\u0995\u09ae\u09be\u09a4\u09cd\u09b0\u09be\u09b0 \u09b8\u09ae\u09c0\u0995\u09b0\u09a3 \u09b8\u09ae\u09cd\u09aa\u09b0\u09cd\u0995\u09c7 \u0986\u09a7\u09c1\u09a8\u09bf\u0995 \u09b8\u09ae\u09be\u09b2\u09cb\u099a\u0995\u09a6\u09c7\u09b0 \u09ac\u09bf\u099a\u09be\u09b0 \u09ac\u09bf\u09b6\u09cd\u09b2\u09c7\u09b7\u09a3<\/strong><\/p>\n<p>\u09ad\u09be\u09b0\u09a4\u09c0\u09df \u0993 \u09ac\u09bf\u09a6\u09c7\u09b6\u09c0 \u0997\u09ac\u09c7\u09b7\u0995\u09b0\u09be \u09aa\u09cd\u09b0\u09a5\u09ae \u0986\u09b0\u09cd\u09af\u09ad\u099f, \u09aa\u09cd\u09b0\u09a5\u09ae \u09ad\u09be\u09b8\u09cd\u0995\u09b0\u09be\u099a\u09be\u09b0\u09cd\u09af, \u09ac\u09cd\u09b0\u09b9\u09cd\u09ae\u0997\u09c1\u09aa\u09cd\u09a4, \u09b6\u09cd\u09b0\u09c0\u09aa\u09a4\u09bf, \u09a6\u09cd\u09ac\u09bf\u09a4\u09c0\u09df \u0986\u09b0\u09cd\u09af\u09ad\u099f, \u09a6\u09cd\u09ac\u09bf\u09a4\u09c0\u09df \u09ad\u09be\u09b8\u09cd\u0995\u09b0\u09be\u099a\u09be\u09b0\u09cd\u09af, \u09a8\u09be\u09b0\u09be\u09df\u09a3, \u0995\u09ae\u09b2\u09be\u0995\u09b0 \u09aa\u09cd\u09b0\u09ae\u09c1\u0996\u09c7\u09b0 \u0995\u09be\u099c\u0997\u09c1\u09b2\u09bf \u09a8\u09bf\u09df\u09c7 \u09ac\u09cd\u09af\u09be\u09aa\u0995 \u09ac\u09bf\u099a\u09be\u09b0 \u09ac\u09bf\u09b6\u09cd\u09b2\u09c7\u09b7\u09a3 \u0995\u09b0\u09c7\u099b\u09c7\u09a8\u0964 \u098f\u0987 \u09ac\u09bf\u099a\u09be\u09b0 \u09ac\u09bf\u09b6\u09cd\u09b2\u09c7\u09b7\u09a3 \u09af\u09be\u0981\u09b0\u09be \u0995\u09b0\u09c7\u099b\u09c7\u09a8 \u09a4\u09be\u0981\u09a6\u09c7\u09b0 \u09ae\u09a7\u09cd\u09af\u09c7 \u0995\u09cb\u09b2\u09c7\u09ac\u09cd\u09b0\u09c1\u0995 (\u09e7\u09ee\u09e7\u09ee \u0996\u09cd\u09b0\u09c0\u0983), \u0995\u09cd\u09af\u09c7 (\u09e7\u09ef\u09e6\u09ee \u0996\u09cd\u09b0\u09c0\u0983), \u098f\u09a8. \u0995\u09c7. \u09ae\u099c\u09c1\u09ae\u09a6\u09be\u09b0 (\u09e7\u09ef\u09e7\u09e7 \u0996\u09cd\u09b0\u09c0\u0983), \u09a1\u09ac\u09cd\u09b2\u09bf\u0989. \u0987. \u0995\u09cd\u09b2\u09be\u09b0\u09cd\u0995 (\u09e7\u09e8\u09e9\u09e6 \u0996\u09cd\u09b0\u09c0\u0983), \u09a8\u09b2\u09bf\u09a8\u09c0 \u09ac\u09bf\u09b9\u09be\u09b0\u09c0 \u09ae\u09bf\u09a4\u09cd\u09b0 (\u09e7\u09ef\u09e7\u09eb \u0996\u09cd\u09b0\u09c0\u0983), \u09ac\u09bf\u09ad\u09c2\u09a4\u09bf\u09ad\u09c2\u09b7\u09a3 \u09a6\u09a4\u09cd\u09a4 (\u09e7\u09ef\u09e9\u09e8 \u0997\u09cd\u09b0\u09c0\u0983), \u09aa\u09cd\u09b0\u09ac\u09cb\u09a7\u099a\u09a8\u09cd\u09a6\u09cd\u09b0 \u09b8\u09c7\u09a8\u0997\u09c1\u09aa\u09cd\u09a4 (\u09e7\u09ef\u09e8\u09ed \u0996\u09cd\u09b0\u09c0\u0983), \u09b0\u09c2\u09aa\u09be\u09b6\u0999\u09cd\u0995\u09b0 \u09b6\u09c1\u0995\u09cd\u09b2\u09be (\u09e7\u09ef\u09ed\u09ee \u0996\u09cd\u09b0\u09c0\u0983), \u0985\u09ae\u09c2\u09b2\u09cd\u09af\u0995\u09c1\u09ae\u09be\u09b0 \u09ac\u09be\u0997 (\u09e7\u09ef\u09ed\u09ed \u0996\u09cd\u09b0\u09c0\u0983), \u09b8\u09be\u09b0\u09a6\u09be\u0995\u09be\u09a8\u09cd\u09a4 \u0997\u09be\u0999\u09cd\u0997\u09c1\u09b2\u09c0 (\u09e7\u09ef\u09e8\u09ed \u0996\u09cd\u09b0\u09c0\u0983), \u09aa\u09cd\u09b0\u09a6\u09c0\u09aa\u0995\u09c1\u09ae\u09be\u09b0 \u09ae\u099c\u09c1\u09ae\u09a6\u09be\u09b0 (\u09e7\u09ef\u09ed\u09ee \u0996\u09cd\u09b0\u09c0\u0983) \u09aa\u09cd\u09b0\u09ae\u09c1\u0996\u09c7\u09b0 \u09a8\u09be\u09ae \u0989\u09b2\u09cd\u09b2\u09c7\u0996\u09af\u09cb\u0997\u09cd\u09af\u0964<\/p>\n<p>\u099c\u09bf. \u0986\u09b0. \u0995\u09cd\u09af\u09c7 \u09a4\u09be\u0981\u09b0 \u0997\u09ac\u09c7\u09b7\u09a3\u09be\u09ae\u09c2\u09b2\u0995 \u09aa\u09cd\u09b0\u09ac\u09a8\u09cd\u09a7\u09c7 (Notes on Indian Mathematics, J. A. S. B., 1908, P 135) \u09aa\u09cd\u09b0\u09a5\u09ae \u0986\u09b0\u09cd\u09af\u09ad\u099f\u09c7\u09b0 \u098f\u0995\u09ae\u09be\u09a4\u09cd\u09b0\u09be\u09b0 \u0985\u09a8\u09bf\u09b0\u09cd\u09a3\u09c7\u09df \u09b8\u09ae\u09c0\u0995\u09b0\u09a3 \u09b8\u09ae\u09cd\u09aa\u09b0\u09cd\u0995\u09c7 \u0986\u09b2\u09cb\u099a\u09a8\u09be \u0995\u09b0\u09c7\u099b\u09c7\u09a8\u0964 \u09a4\u09bf\u09a8\u09bf \u09a4\u09be\u0981\u09b0 \u09aa\u09cd\u09b0\u09ac\u09a8\u09cd\u09a7\u09c7\u09b0 \u098f\u0995 \u099c\u09be\u09df\u0997\u09be\u09df \u09ac\u09b2\u09c7\u099b\u09c7\u09a8, &#8220;It was thought that the special treatment of indeterminate equation was of Indian Origin. Colebroke, Woepcks, Chasles and Rodet seemed to think so, and the conclusions of such eminent scholars can not be altogether ignored. But Colebroke, Woepecks and Chasles attributed the discovery to Brahmagupta and in this were obviously wrong.<\/p>\n<p>They had only very vague ideas about Aryabhata whose works were not available in their times. While Rodet was misled by the later commentaries \u0995\u09cd\u09af\u09c7 \u09b6\u09c7\u09b7\u09c7 \u09ae\u09a8\u09cd\u09a4\u09ac\u09cd\u09af \u0995\u09b0\u09c7\u09a8 &#8221; These results which are vaguely embodied in Aryabhata&#8217;s rule may of course, be put in perfectly general form.<\/p>\n<p>\u09a1\u09bf. \u0987. \u09b8\u09cd\u09ae\u09c0\u09a5 \u09a4\u09be\u0981\u09b0 \u09ac\u09bf\u0996\u09cd\u09af\u09be\u09a4 \u0997\u09cd\u09b0\u09a8\u09cd\u09a5\u09c7\u09b0 (History of Mathematics, Vol-1 P-156) \u098f\u0995 \u099c\u09be\u09df\u0997\u09be\u09df \u09ac\u09b2\u09c7\u099b\u09c7\u09a8-\u098f\u0995 \u09ae\u09be\u09a4\u09cd\u09b0\u09be\u09b0 \u0985\u09a8\u09bf\u09b0\u09cd\u09a3\u09c7\u09df \u09b8\u09ae\u09c0\u0995\u09b0\u09a3\u09c7\u09b0 \u09b8\u09ae\u09be\u09a7\u09be\u09a8\u09c7 \u0986\u09b0\u09cd\u09af\u09ad\u099f \u09ac\u09bf\u09a4\u09a4 \u09ad\u0997\u09cd\u09a8\u09be\u0982\u09b6\u09c7\u09b0 (Continued fraction) \u09aa\u09a6\u09cd\u09a7\u09a4\u09bf \u09aa\u09cd\u09b0\u09df\u09cb\u0997 \u0995\u09b0\u09a4\u09c7 \u09b8\u099a\u09c7\u09b7\u09cd\u099f \u09b9\u09df\u09c7\u099b\u09bf\u09b2\u09c7\u09a8\u0964<\/p>\n<p><strong>(\u099a\u09b2\u09ac\u09c7)<\/strong><\/p>\n<h4 class=\"single-page-title\">\u09aa\u09cd\u09b0\u09be\u099a\u09c0\u09a8 \u09ad\u09be\u09b0\u09a4\u09c7 \u0997\u09a3\u09bf\u09a4\u099a\u09b0\u09cd\u099a\u09be (\u09aa\u09b0\u09cd\u09ac-\u09e8\u09ef\u09e9)<\/h4>\n<blockquote class=\"wp-embedded-content\" data-secret=\"KX2Uy6P8VJ\"><p><a href=\"https:\/\/sarakhon.com\/?p=92272\">\u09aa\u09cd\u09b0\u09be\u099a\u09c0\u09a8 \u09ad\u09be\u09b0\u09a4\u09c7 \u0997\u09a3\u09bf\u09a4\u099a\u09b0\u09cd\u099a\u09be (\u09aa\u09b0\u09cd\u09ac-\u09e8\u09ef\u09e9)<\/a><\/p><\/blockquote>\n<p><iframe loading=\"lazy\" class=\"wp-embedded-content\" sandbox=\"allow-scripts\" security=\"restricted\" style=\"position: absolute; visibility: hidden;\" title=\"&#8220;\u09aa\u09cd\u09b0\u09be\u099a\u09c0\u09a8 \u09ad\u09be\u09b0\u09a4\u09c7 \u0997\u09a3\u09bf\u09a4\u099a\u09b0\u09cd\u099a\u09be (\u09aa\u09b0\u09cd\u09ac-\u09e8\u09ef\u09e9)&#8221; &#8212; Sarakhon \u0964 \u09b8\u09be\u09b0\u09be\u0995\u09cd\u09b7\u09a3\" src=\"https:\/\/sarakhon.com\/?p=92272&#038;embed=true#?secret=hSF0pkkk8o#?secret=KX2Uy6P8VJ\" data-secret=\"KX2Uy6P8VJ\" width=\"500\" height=\"282\" frameborder=\"0\" marginwidth=\"0\" marginheight=\"0\" scrolling=\"no\"><\/iframe><\/p>\n<p>&nbsp;<\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u09ad\u09be\u09b0\u09a4\u09c0\u09df \u098f\u0995\u09ae\u09be\u09a4\u09cd\u09b0\u09be\u09b0 \u09b8\u09ae\u09c0\u0995\u09b0\u09a3 \u09b8\u09ae\u09cd\u09aa\u09b0\u09cd\u0995\u09c7 \u0986\u09a7\u09c1\u09a8\u09bf\u0995 \u09b8\u09ae\u09be\u09b2\u09cb\u099a\u0995\u09a6\u09c7\u09b0 \u09ac\u09bf\u099a\u09be\u09b0 \u09ac\u09bf\u09b6\u09cd\u09b2\u09c7\u09b7\u09a3 \u09ad\u09be\u09b0\u09a4\u09c0\u09df \u0993 \u09ac\u09bf\u09a6\u09c7\u09b6\u09c0 \u0997\u09ac\u09c7\u09b7\u0995\u09b0\u09be \u09aa\u09cd\u09b0\u09a5\u09ae \u0986\u09b0\u09cd\u09af\u09ad\u099f, \u09aa\u09cd\u09b0\u09a5\u09ae \u09ad\u09be\u09b8\u09cd\u0995\u09b0\u09be\u099a\u09be\u09b0\u09cd\u09af, \u09ac\u09cd\u09b0\u09b9\u09cd\u09ae\u0997\u09c1\u09aa\u09cd\u09a4, \u09b6\u09cd\u09b0\u09c0\u09aa\u09a4\u09bf, \u09a6\u09cd\u09ac\u09bf\u09a4\u09c0\u09df \u0986\u09b0\u09cd\u09af\u09ad\u099f, \u09a6\u09cd\u09ac\u09bf\u09a4\u09c0\u09df \u09ad\u09be\u09b8\u09cd\u0995\u09b0\u09be\u099a\u09be\u09b0\u09cd\u09af, \u09a8\u09be\u09b0\u09be\u09df\u09a3, \u0995\u09ae\u09b2\u09be\u0995\u09b0 \u09aa\u09cd\u09b0\u09ae\u09c1\u0996\u09c7\u09b0 \u0995\u09be\u099c\u0997\u09c1\u09b2\u09bf \u09a8\u09bf\u09df\u09c7 \u09ac\u09cd\u09af\u09be\u09aa\u0995 \u09ac\u09bf\u099a\u09be\u09b0 \u09ac\u09bf\u09b6\u09cd\u09b2\u09c7\u09b7\u09a3 \u0995\u09b0\u09c7\u099b\u09c7\u09a8\u0964 \u098f\u0987 \u09ac\u09bf\u099a\u09be\u09b0 \u09ac\u09bf\u09b6\u09cd\u09b2\u09c7\u09b7\u09a3 \u09af\u09be\u0981\u09b0\u09be \u0995\u09b0\u09c7\u099b\u09c7\u09a8 \u09a4\u09be\u0981\u09a6\u09c7\u09b0 \u09ae\u09a7\u09cd\u09af\u09c7 \u0995\u09cb\u09b2\u09c7\u09ac\u09cd\u09b0\u09c1\u0995 (\u09e7\u09ee\u09e7\u09ee \u0996\u09cd\u09b0\u09c0\u0983), \u0995\u09cd\u09af\u09c7 (\u09e7\u09ef\u09e6\u09ee \u0996\u09cd\u09b0\u09c0\u0983), \u098f\u09a8. \u0995\u09c7. \u09ae\u099c\u09c1\u09ae\u09a6\u09be\u09b0 (\u09e7\u09ef\u09e7\u09e7 \u0996\u09cd\u09b0\u09c0\u0983), \u09a1\u09ac\u09cd\u09b2\u09bf\u0989. \u0987. \u0995\u09cd\u09b2\u09be\u09b0\u09cd\u0995 (\u09e7\u09e8\u09e9\u09e6 \u0996\u09cd\u09b0\u09c0\u0983), \u09a8\u09b2\u09bf\u09a8\u09c0 [&hellip;]<\/p>\n","protected":false},"author":5,"featured_media":93005,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[38,17],"tags":[],"location":[],"class_list":["post-93004","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-38","category-17"],"cmb2":{"heading_information":{"sub_title":""},"reporter_information":{"video":"","reporter_name":"\u09aa\u09cd\u09b0\u09a6\u09c0\u09aa \u0995\u09c1\u09ae\u09be\u09b0 \u09ae\u099c\u09c1\u09ae\u09a6\u09be\u09b0"},"audio_information":{"audio_link":"","audio_link_id":""},"seo_information":{"meta_keyword":""}},"_links":{"self":[{"href":"https:\/\/sarakhon.com\/index.php?rest_route=\/wp\/v2\/posts\/93004","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/sarakhon.com\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/sarakhon.com\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/sarakhon.com\/index.php?rest_route=\/wp\/v2\/users\/5"}],"replies":[{"embeddable":true,"href":"https:\/\/sarakhon.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=93004"}],"version-history":[{"count":1,"href":"https:\/\/sarakhon.com\/index.php?rest_route=\/wp\/v2\/posts\/93004\/revisions"}],"predecessor-version":[{"id":93006,"href":"https:\/\/sarakhon.com\/index.php?rest_route=\/wp\/v2\/posts\/93004\/revisions\/93006"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/sarakhon.com\/index.php?rest_route=\/wp\/v2\/media\/93005"}],"wp:attachment":[{"href":"https:\/\/sarakhon.com\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=93004"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/sarakhon.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=93004"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/sarakhon.com\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=93004"},{"taxonomy":"location","embeddable":true,"href":"https:\/\/sarakhon.com\/index.php?rest_route=%2Fwp%2Fv2%2Flocation&post=93004"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}