{"id":3615,"date":"2026-03-21T01:58:51","date_gmt":"2026-03-21T01:58:51","guid":{"rendered":"https:\/\/npk1169-001-site1.mtempurl.com\/?p=3615"},"modified":"2026-04-19T11:19:33","modified_gmt":"2026-04-19T11:19:33","slug":"negative-numbers-rina","status":"publish","type":"post","link":"https:\/\/www.bharatwisdom.com\/hi\/mathematics\/negative-numbers-rina\/","title":{"rendered":"\u090b\u0923\u093e\u0924\u094d\u092e\u0915 \u0938\u0902\u0916\u094d\u092f\u093e\u090f\u0901 (\u0930\u0940\u0928\u093e) \u2013 \u090b\u0923 \u0915\u093e \u0917\u0923\u093f\u0924"},"content":{"rendered":"<div class=\"fusion-fullwidth fullwidth-box fusion-builder-row-1 fusion-flex-container nonhundred-percent-fullwidth non-hundred-percent-height-scrolling\" style=\"--awb-border-radius-top-left:0px;--awb-border-radius-top-right:0px;--awb-border-radius-bottom-right:0px;--awb-border-radius-bottom-left:0px;--awb-flex-wrap:wrap;\" ><div class=\"fusion-builder-row fusion-row fusion-flex-align-items-flex-start fusion-flex-content-wrap\" style=\"max-width:1279.2px;margin-left: calc(-4% \/ 2 );margin-right: calc(-4% \/ 2 );\"><div class=\"fusion-layout-column fusion_builder_column fusion-builder-column-0 fusion_builder_column_1_1 1_1 fusion-flex-column\" style=\"--awb-bg-size:cover;--awb-width-large:100%;--awb-margin-top-large:0px;--awb-spacing-right-large:1.92%;--awb-margin-bottom-large:0px;--awb-spacing-left-large:1.92%;--awb-width-medium:100%;--awb-spacing-right-medium:1.92%;--awb-spacing-left-medium:1.92%;--awb-width-small:100%;--awb-spacing-right-small:1.92%;--awb-spacing-left-small:1.92%;\"><div class=\"fusion-column-wrapper fusion-flex-justify-content-flex-start fusion-content-layout-column\"><div class=\"fusion-text fusion-text-1\"><p id=\"p-rc_ed88986f39805c81-256\" data-path-to-node=\"80\"><span data-path-to-node=\"80,0\"><b data-path-to-node=\"80,0\" data-index-in-node=\"0\">\u0905\u0935\u0927\u093e\u0930\u0923\u093e<\/b> <\/span><span data-path-to-node=\"80,2\"><span class=\"citation-918\">\u090b\u0923\u093e\u0924\u094d\u092e\u0915 \u0938\u0902\u0916\u094d\u092f\u093e\u090f\u0901 (-1, -5 \u0914\u0930 -10) \u0936\u0942\u0928\u094d\u092f \u0938\u0947 \u0915\u092e \u0939\u094b\u0924\u0940 \u0939\u0948\u0902\u0964<\/span><\/span><span data-path-to-node=\"80,4\">. <\/span><span data-path-to-node=\"80,6\"><span class=\"citation-917\">\u092f\u0947 \u090b\u0923, \u0939\u093f\u092e\u093e\u0902\u0915 \u0938\u0947 \u0928\u0940\u091a\u0947 \u0915\u0947 \u0924\u093e\u092a\u092e\u093e\u0928 \u0914\u0930 \u0935\u093f\u092a\u0930\u0940\u0924 \u0926\u093f\u0936\u093e\u0913\u0902 \u0915\u094b \u0926\u0930\u094d\u0936\u093e\u0928\u0947 \u0915\u0947 \u0932\u093f\u090f \u0909\u092a\u092f\u094b\u0917\u0940 \u0939\u0948\u0902\u0964<\/span><\/span><span data-path-to-node=\"80,8\">.<\/span><\/p>\n<p id=\"p-rc_ed88986f39805c81-257\" data-path-to-node=\"81\"><span data-path-to-node=\"81,0\"><b data-path-to-node=\"81,0\" data-index-in-node=\"0\">\u0915\u0939\u093e\u0928\u0940<\/b> <\/span><span data-path-to-node=\"81,2\"><span class=\"citation-916\">\u092a\u0941\u0928\u0930\u094d\u091c\u093e\u0917\u0930\u0923 \u0915\u093e\u0932 \u0915\u0947 \u0917\u0923\u093f\u0924\u091c\u094d\u091e\u094b\u0902 \u0915\u0947 \u0932\u093f\u090f, &quot;\u090b\u0923\u093e\u0924\u094d\u092e\u0915&quot; \u0938\u0902\u0916\u094d\u092f\u093e \u0915\u093e \u0935\u093f\u091a\u093e\u0930 \u092c\u0947\u0924\u0941\u0915\u093e \u0925\u093e - \u0906\u092a\u0915\u0947 \u092a\u093e\u0938 \u0936\u0942\u0928\u094d\u092f \u0938\u0947 \u0915\u092e \u0915\u0948\u0938\u0947 \u0939\u094b \u0938\u0915\u0924\u093e \u0939\u0948?<\/span><\/span><span data-path-to-node=\"81,4\">. <\/span><span data-path-to-node=\"81,6\"><span class=\"citation-915\">\u0909\u0928\u094d\u0939\u094b\u0902\u0928\u0947 \u0907\u0928 \u092a\u0930\u093f\u0923\u093e\u092e\u094b\u0902 \u0915\u094b &quot;\u091d\u0942\u0920\u093e&quot; \u092f\u093e &quot;\u092e\u0928\u0917\u0922\u093c\u0902\u0924&quot; \u092c\u0924\u093e\u092f\u093e\u0964\u201c<\/span><\/span><span data-path-to-node=\"81,8\">. <\/span><span data-path-to-node=\"81,10\"><span class=\"citation-914\">\u0932\u0947\u0915\u093f\u0928 \u092d\u093e\u0930\u0924\u0940\u092f \u092e\u093e\u0928\u0938\u093f\u0915\u0924\u093e \u0905\u0927\u093f\u0915 \u0935\u094d\u092f\u093e\u0935\u0939\u093e\u0930\u093f\u0915 \u0925\u0940\u0964<\/span><\/span><span data-path-to-node=\"81,12\">. <\/span><span data-path-to-node=\"81,14\"><span class=\"citation-913\">\u0927\u0928 \u0914\u0930 \u090b\u0923 \u0915\u0947 \u0938\u0930\u0932 \u0924\u0930\u094d\u0915 \u0915\u093e \u0909\u092a\u092f\u094b\u0917 \u0915\u0930\u0924\u0947 \u0939\u0941\u090f, \u092c\u094d\u0930\u0939\u094d\u092e\u0917\u0941\u092a\u094d\u0924 \u0928\u0947 \u092e\u0939\u0938\u0942\u0938 \u0915\u093f\u092f\u093e \u0915\u093f \u0917\u0923\u093f\u0924 \u0920\u0940\u0915 \u090f\u0915 \u092c\u0939\u0940\u0916\u093e\u0924\u0947 \u0915\u0940 \u0924\u0930\u0939 \u0915\u093e\u092e \u0915\u0930\u0924\u093e \u0939\u0948\u0964<\/span><\/span><span data-path-to-node=\"81,16\">. <\/span><span data-path-to-node=\"81,18\"><span class=\"citation-912\">\u0909\u0928\u094d\u0939\u094b\u0902\u0928\u0947 \u0939\u0940 \u0938\u092c\u0938\u0947 \u092a\u0939\u0932\u0947 \u0909\u0938 \u0928\u093f\u092f\u092e \u0915\u094b \u0932\u093f\u0916\u093e \u0925\u093e \u091c\u093f\u0938\u0947 \u0939\u092e \u0938\u092d\u0940 \u092a\u094d\u0930\u093e\u0925\u092e\u093f\u0915 \u0935\u093f\u0926\u094d\u092f\u093e\u0932\u092f \u092e\u0947\u0902 \u0938\u0940\u0916\u0924\u0947 \u0939\u0948\u0902: &quot;\u0926\u094b \u090b\u0923\u094b\u0902 \u0915\u093e \u0917\u0941\u0923\u0928\u092b\u0932 \u090f\u0915 \u0938\u0902\u092a\u0924\u094d\u0924\u093f \u0939\u094b\u0924\u093e \u0939\u0948&quot; (\u090b\u0923\u093e\u0924\u094d\u092e\u0915 x \u090b\u0923\u093e\u0924\u094d\u092e\u0915 = \u0927\u0928\u093e\u0924\u094d\u092e\u0915)\u0964<\/span><\/span><span data-path-to-node=\"81,20\">. <\/span><span data-path-to-node=\"81,22\"><span class=\"citation-911\">\u090b\u0923 \u0915\u094b \u090f\u0915 \u0917\u0923\u093f\u0924\u0940\u092f \u0935\u093e\u0938\u094d\u0924\u0935\u093f\u0915\u0924\u093e \u0915\u0947 \u0930\u0942\u092a \u092e\u0947\u0902 \u092e\u093e\u0928\u0915\u0930, \u092d\u093e\u0930\u0924 \u0928\u0947 \u0906\u0927\u0941\u0928\u093f\u0915 \u0935\u093f\u0924\u094d\u0924 \u0914\u0930 \u0935\u093f\u0926\u094d\u092f\u0941\u0924 \u0905\u092d\u093f\u092f\u093e\u0902\u0924\u094d\u0930\u093f\u0915\u0940 \u0915\u0940 \u0928\u0940\u0902\u0935 \u0926\u0941\u0928\u093f\u092f\u093e \u0915\u094b \u0926\u0940\u0964<\/span><\/span><span data-path-to-node=\"81,24\">.<\/span><\/p>\n<p data-path-to-node=\"82\"><b data-path-to-node=\"82\" data-index-in-node=\"0\">\u0938\u092e\u092f\u0930\u0947\u0916\u093e<\/b><\/p>\n<table data-path-to-node=\"83\">\n<thead>\n<tr>\n<td><strong>\u092e\u0940\u0932 \u0915\u093e \u092a\u0924\u094d\u0925\u0930<\/strong><\/td>\n<td><strong>\u0935\u093f\u0935\u0930\u0923<\/strong><\/td>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<td><span data-path-to-node=\"83,1,0,0\"><b data-path-to-node=\"83,1,0,0\" data-index-in-node=\"0\">\u092a\u0936\u094d\u091a\u093f\u092e\u0940 \u0938\u0902\u0926\u0930\u094d\u092d.<\/b><\/span><\/td>\n<td>\n<p id=\"p-rc_ed88986f39805c81-258\" data-path-to-node=\"83,1,1,0\"><span data-path-to-node=\"83,1,1,0,1\"><span class=\"citation-910\">1600 \u0908\u0938\u094d\u0935\u0940 (\u092f\u0942\u0930\u094b\u092a \u092e\u0947\u0902 \u0905\u0928\u093f\u091a\u094d\u091b\u093e \u0938\u0947 \u0938\u094d\u0935\u0940\u0915\u093e\u0930 \u0915\u093f\u092f\u093e \u0917\u092f\u093e) <\/span><\/span><\/p>\n<div class=\"source-inline-chip-container ng-star-inserted\"><\/div>\n<\/td>\n<\/tr>\n<tr>\n<td><span data-path-to-node=\"83,2,0,0\"><b data-path-to-node=\"83,2,0,0\" data-index-in-node=\"0\">\u092d\u093e\u0930\u0924\u0940\u092f \u0938\u094d\u0930\u094b\u0924<\/b><\/span><\/td>\n<td>\n<p id=\"p-rc_ed88986f39805c81-259\" data-path-to-node=\"83,2,1,0\"><span data-path-to-node=\"83,2,1,0,0\">628 \u0908\u0938\u094d\u0935\u0940 (\u092c\u094d\u0930\u0939\u094d\u092e\u0917\u0941\u092a\u094d\u0924); <\/span><span data-path-to-node=\"83,2,1,0,2\"><span class=\"citation-909\">200 \u0908\u0938\u093e \u092a\u0942\u0930\u094d\u0935 \u0938\u0947 \u092a\u0939\u0932\u0947 (\u092c\u0916\u094d\u0936\u093e\u0932\u0940 \u092a\u093e\u0902\u0921\u0941\u0932\u093f\u092a\u093f) <\/span><\/span><\/p>\n<div class=\"source-inline-chip-container ng-star-inserted\"><\/div>\n<\/td>\n<\/tr>\n<tr>\n<td><span data-path-to-node=\"83,3,0,0\"><b data-path-to-node=\"83,3,0,0\" data-index-in-node=\"0\">\u0915\u093e\u0932 \u0905\u0902\u0924\u0930\u093e\u0932<\/b><\/span><\/td>\n<td>\n<p id=\"p-rc_ed88986f39805c81-260\" data-path-to-node=\"83,3,1,0\"><span data-path-to-node=\"83,3,1,0,1\"><span class=\"citation-908\">\u090f\u0915 \u0939\u091c\u093e\u0930 \u0938\u093e\u0932 \u0938\u0947 \u092d\u0940 \u0905\u0927\u093f\u0915 <\/span><\/span><\/p>\n<div class=\"source-inline-chip-container ng-star-inserted\"><\/div>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p data-path-to-node=\"84\"><b data-path-to-node=\"84\" data-index-in-node=\"0\">\u0938\u092c\u0942\u0924<\/b><\/p>\n<blockquote data-path-to-node=\"85\">\n<p id=\"p-rc_ed88986f39805c81-261\" data-path-to-node=\"85,0\"><span data-path-to-node=\"85,0,0\"><b data-path-to-node=\"85,0,0\" data-index-in-node=\"0\">\u0938\u0902\u0938\u094d\u0915\u0943\u0924 \u0936\u094d\u0932\u094b\u0915:<\/b> \u090b\u0923\u092e\u0943\u0923\u0947\u0928 \u0927\u0928\u0902 \u0938\u094d\u092f\u093e\u0926\u094d \u0927\u0928\u0902 \u0927\u0928\u0947\u0928 \u0927\u0928\u0902 \u092d\u0935\u0947\u0924\u094d\u0964 <\/span><span data-path-to-node=\"85,0,2\"><span class=\"citation-907\">\u090b\u0923\u092f\u094b\u0930\u094d\u090b\u0923\u0902 \u0938\u094d\u092f\u093e\u0924\u094d \u090b\u0923\u0902 \u091a \u0927\u0928\u094d\u092e\u0943\u0923\u092f\u094b\u0936\u094d\u091a \u0965 <\/span><\/span><span data-path-to-node=\"85,0,4\"> <b data-path-to-node=\"85,0,4\" data-index-in-node=\"1\">\u0932\u093f\u092a\u094d\u092f\u0902\u0924\u0930\u0923:<\/b> \u0927\u0928\u092e\u0943\u0923\u0947\u0928 \u0927\u0928\u0902 \u0938\u094d\u092f\u093e\u0926\u094d \u0927\u0928\u0902 \u0927\u0928\u0947\u0928 \u0927\u0928\u0902 \u092d\u0935\u0947\u0924\u094d | \u090b\u0923\u093e\u0927\u0928\u092f\u094b\u0930\u094d\u092e\u093e\u0923\u0902 \u0938\u094d\u092f\u093e\u0924\u094d \u090b\u0923\u0902 \u091a \u0927\u0928\u094d\u092e\u0943\u0923\u092f\u094b\u0936\u094d\u091a || <\/span><span data-path-to-node=\"85,0,6\"><span class=\"citation-906\">\u092c\u094d\u0930\u0939\u094d\u092e\u0938\u094d\u092b\u0941\u091f\u0938\u093f\u0926\u094d\u0927\u093e\u0902\u0924 (18.30) (\u0930\u093e\u0936\u093f\u092f\u094b\u0902 \u0915\u0947 \u0932\u093f\u090f \u0928\u093f\u092f\u092e)\u0964. <\/span><\/span><span data-path-to-node=\"85,0,9\"><b data-path-to-node=\"85,0,9\" data-index-in-node=\"0\"><span class=\"citation-905\">\u0905\u0930\u094d\u0925:<\/span><\/b><span class=\"citation-905\"> \u201c\u090b\u0923 \u0915\u094b \u090b\u0923 \u0938\u0947 \u0917\u0941\u0923\u093e \u0915\u0930\u0928\u0947 \u092a\u0930 \u0927\u0928 \u092a\u094d\u0930\u093e\u092a\u094d\u0924 \u0939\u094b\u0924\u093e \u0939\u0948 (\u090b\u0923\u093e\u0924\u094d\u092e\u0915 \u00d7 \u090b\u0923\u093e\u0924\u094d\u092e\u0915 = \u0927\u0928\u093e\u0924\u094d\u092e\u0915)\u0964 \u0927\u0928 \u0915\u094b \u0927\u0928 \u0938\u0947 \u0917\u0941\u0923\u093e \u0915\u0930\u0928\u0947 \u092a\u0930 \u0927\u0928 \u092a\u094d\u0930\u093e\u092a\u094d\u0924 \u0939\u094b\u0924\u093e \u0939\u0948\u0964 \u090b\u0923 \u0915\u094b \u0927\u0928 \u0938\u0947 \u0917\u0941\u0923\u093e \u0915\u0930\u0928\u0947 \u092a\u0930 \u090b\u0923 \u0939\u0940 \u092a\u094d\u0930\u093e\u092a\u094d\u0924 \u0939\u094b\u0924\u093e \u0939\u0948\u0964\u201d <\/span><\/span><\/p>\n<div class=\"source-inline-chip-container ng-star-inserted\"><\/div>\n<\/blockquote>\n<p id=\"p-rc_ed88986f39805c81-262\" data-path-to-node=\"86\"><span data-path-to-node=\"86,0\"><b data-path-to-node=\"86,0\" data-index-in-node=\"0\">\u0938\u0902\u092c\u0902\u0927\u093f\u0924 \u0928\u0935\u093e\u091a\u093e\u0930<\/b> <\/span><span data-path-to-node=\"86,2\"><span class=\"citation-904\">\u092c\u0916\u094d\u0936\u093e\u0932\u0940 \u092a\u093e\u0902\u0921\u0941\u0932\u093f\u092a\u093f \u092e\u0947\u0902 \u090b\u0923\u093e\u0924\u094d\u092e\u0915 \u092a\u0942\u0930\u094d\u0923\u093e\u0902\u0915\u094b\u0902 \u0915\u094b \u0926\u0930\u094d\u0936\u093e\u0928\u0947 \u0915\u0947 \u0932\u093f\u090f \u092c\u093f\u0902\u0926\u0941 \u0915\u093e \u092a\u094d\u0930\u092f\u094b\u0917 \u0915\u093f\u092f\u093e \u0917\u092f\u093e \u0925\u093e \u0914\u0930 \u0907\u0938\u092e\u0947\u0902 \u0915\u0939\u093e \u0917\u092f\u093e \u0925\u093e \u0915\u093f \u0936\u0942\u0928\u094d\u092f \u090f\u0915 \u0927\u0928\u093e\u0924\u094d\u092e\u0915 \u0938\u0902\u0916\u094d\u092f\u093e \u0914\u0930 \u0909\u0938\u0915\u0947 \u090b\u0923\u093e\u0924\u094d\u092e\u0915 \u0915\u093e \u092f\u094b\u0917 \u0939\u0948 (X + (-X) = 0)\u0964<\/span><\/span><span data-path-to-node=\"86,4\">.<\/span><\/p>\n<p id=\"p-rc_ed88986f39805c81-263\" data-path-to-node=\"87\"><span data-path-to-node=\"87,0\"><b data-path-to-node=\"87,0\" data-index-in-node=\"0\">\u0906\u0927\u0941\u0928\u093f\u0915 \u0935\u093f\u0930\u093e\u0938\u0924<\/b> <\/span><span data-path-to-node=\"87,2\"><span class=\"citation-903\">\u0906\u0927\u0941\u0928\u093f\u0915 \u0935\u093f\u0924\u094d\u0924, \u0938\u0926\u093f\u0936 \u092d\u094c\u0924\u093f\u0915\u0940 \u0914\u0930 \u0935\u093f\u0926\u094d\u092f\u0941\u0924 \u0905\u092d\u093f\u092f\u093e\u0902\u0924\u094d\u0930\u093f\u0915\u0940 (\u0927\u0928\u093e\u0924\u094d\u092e\u0915 \u0914\u0930 \u090b\u0923\u093e\u0924\u094d\u092e\u0915 \u0926\u094b\u0928\u094b\u0902 \u0906\u0935\u0947\u0936\u094b\u0902) \u0915\u0947 \u0932\u093f\u090f \u090b\u0923\u093e\u0924\u094d\u092e\u0915 \u0938\u0902\u0916\u094d\u092f\u093e\u090f\u0901 \u0906\u0935\u0936\u094d\u092f\u0915 \u0939\u0948\u0902\u0964<\/span><\/span><span data-path-to-node=\"87,4\">.<\/span><\/p>\n<\/div><\/div><\/div><\/div><\/div>","protected":false},"excerpt":{"rendered":"","protected":false},"author":1,"featured_media":3505,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_acf_changed":false,"footnotes":""},"categories":[74],"tags":[544,590,577,578,589,587,588],"class_list":["post-3615","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-mathematics","tag-ancient-indian-mathematics","tag-bakhshali-manuscript","tag-brahmagupta","tag-brahmasphutasiddhanta","tag-dhana","tag-negative-numbers","tag-rina"],"acf":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v27.4 - 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