![sm_18_01_1_03.gif](\"http:\/\/blog.jackjia.com\/wp-content\/uploads\/2008\/11\/sm_18_01_1_03.gif\")
\n\u56fe\u4e09\uff1a\u5370\u5ea6\u963f\u62c9\u4f2f\u6570\u5b57\u7684\u6f14\u53d8\u7cfb\u8c31 <\/p>\n
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\u4ece Gupta \u738b\u671d\u7684\u665a\u671f\u5f00\u59cb\uff0c\u5370\u5ea6\u53c8\u4e00\u518d\u53d7\u5230\u5916\u65cf\u5165\u4fb5\u3001\u5185\u90e8\u7eb7\u4e89\u7684\u5f71\u54cd\u3002\u4ece\u6765\u5c31\u6ca1\u6709\u72ec\u7acb\u7edf\u4e00\u7684\u5c40\u9762\u3002\u7136\u800c\u4ece\u516d\u4e16\u7eaa\u5f00\u59cb\u5230\u5341\u4e8c\u4e16\u7eaa\u4e3a\u6b62\uff0c\u5374\u4ea7\u751f\u4e86\u51e0\u4f4d\u503c\u5f97\u6ce8\u610f\u7684\u6570\u5b66\u5bb6\uff0c\u5982 Aryabhata\uff08\u516d\u4e16\u7eaa\uff09\u3001Varahamihira\uff08\u516d\u4e16\u7eaa\uff09\u3001Brahmagupta\uff08\u4e03\u4e16\u7eaa\uff09\u3001Mahavira\uff08\u4e5d\u4e16\u7eaa\uff09\u3001Bhaskara\uff08\u5341\u4e8c\u4e16\u7eaa\uff09\u7b49\u3002 <\/p>\n
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\u7136\u800c\u5370\u5ea6\u7684\u4f20\u7edf\u6570\u5b66\u5728\u7b97\u672f\u53ca\u4ee3\u6570\u65b9\u9762\u5219\u6709\u76f8\u5f53\u7684\u6210\u5c31\uff1b\u8fd9\u4e9b\u5305\u62ec\u5efa\u7acb\u5b8c\u6574\u7684\u5341\u8fdb\u4f4d\u8bb0\u6570\u7cfb\u7edf\uff0c\u5f15\u8fdb\u8d1f\u6570\u7684\u89c2\u5ff5\u53ca\u8ba1\u7b97\uff0c\u4f7f\u4ee3\u6570\u534a\u7b26\u53f7\u5316\uff0c\u63d0\u4f9b\u5f00\u65b9\u7684\u65b9\u6cd5\uff0c\u89e3\u4e8c\u6b21\u65b9\u7a0b\u5f0f\u53ca\u4e00\u6b21\u4e0d\u5b9a\u65b9\u7a0b\u5f0f\u7b49\u3002<\/p>\n
\u5370\u5ea6\u4eba\u8981\u9648\u8ff0\u6570\u5b66\u9898\u76ee\u65f6\uff0c\u5e38\u628a\u5b83\u5f04\u5f97\u5e7b\u60f3\u6709\u8da3\uff0c\u6216\u8005\u7f16\u6210\u8bd7\u53e5\uff0c\u6216\u8005\u52a0\u4e0a\u5386\u53f2\u80cc\u666f\uff0c\u4f7f\u5f97\u9898\u76ee\u80fd\u591f\u5438\u5f15\u4eba\u3002\u4e0b\u9762\u662f\u4e2a\u4f8b\u5b50\uff1a <\/p>\n
\u5728\u67d0\u4e2a\u7edd\u58c1\u9876\u4e0a\uff0c\u4f4f\u7740\u4e24\u4f4d\u82e6\u884c\u8005\u3002\u5176\u4e2d\u4e00\u4f4d\u56e0\u62e5\u6709\u5996\u672f\uff0c\u53ef\u4ee5\u5728\u7a7a\u4e2d\u884c\u8d70\u3002\u4ed6\u4ece\u5c71\u9876\u5782\u76f4\u5347\u7a7a\u4e00\u6bb5\u8ddd\u79bb\uff0c\u7136\u540e\u5bf9\u51c6\u67d0\u4e00\u5c0f\u9547\u2018\u8d70\u2019\u53bb\u3002\u53e6\u4e00\u4f4d\u82e6\u884c\u8005\uff0c\u5219\u4ece\u5c71\u9876\u4e0a\u4e0b\u6765\uff0c\u518d\u5411\u5c0f\u9547\u8d70\u53bb\u3002\u7ed3\u679c\u4e24\u8005\u7684\u8ddd\u79bb\u76f8\u540c\u3002\u5047\u8bbe\u2026\u2026\uff0c\u95ee\u2026\u2026\uff1f
\n\u53e6\u4e00\u4e2a\u4f8b\u5b50\uff1a <\/p>\n
\u25b3
\n\u6797\u5b50\u91cc\u5934\u6811\u6728\u7e41\u8302
\n\u7d2f\u7d2f\u82b1\u679c\u6811\u679d\u62c2\u5730
\n\u67e0\u6aac\u9999\u8549\u68d5\u6988\u8292\u679c
\n\u9e66\u9e49\u5e03\u8c37\u53eb\u58f0\u4e0d\u7edd
\n\u6c60\u5858\u83b2\u82b1\u871c\u8702\u73af\u7ed5
\n\u75b2\u7d2f\u65c5\u8005\u6b23\u7136\u5165\u6797
\n\u25bd <\/p>\n
\u4eca\u6709 63 \u5806\u6570\u76ee\u76f8\u540c\u7684\u9999\u8549\uff0c\u53e6\u52a07\u6839\u9999\u8549\uff0c\u5e73\u5747\u5206\u7ed9 23 \u4f4d\u65c5\u8005\uff0c\u521a\u597d\u5206\u5b8c\u3002\u8bf7\u95ee\u4e00\u5806\u9999\u8549\u8981\u6709\u591a\u5c11\u6839\uff1f
\n\u5982\u679c\u6bcf\u5806\u9999\u8549\u6709 x \u6839\uff0c\u6bcf\u4eba\u5206\u5f97 y \u6839\uff0c\u90a3\u4e48\u8981\u89e3\u7684\u5c31\u662f 63x+7=23y \u8fd9\u6837\u7684\u4e8c\u5143\u4e00\u6b21\u4e0d\u5b9a\u65b9\u7a0b\u5f0f\u3002\u4ed6\u4eec\u7684\u89e3\u6cd5\u662f\u8fd9\u6837\u7684\uff1a\u5c06 63 \u4e0e 23 \u505a\u8f97\u8f6c\u76f8\u9664<\/p>\n
\u2026\u2026<\/p>\n
\u7136\u540e\u6839\u636e\u76f8\u9664\u7684\u7ed3\u679c\u628a 63\/23 \u5199\u6210\u8fde\u5206\u6570 <\/p>\n
\u2026\u2026<\/p>\n
\u5c06\u6700\u540e\u7684 1\/5 \u53bb\u6389\uff0c\u5219\u53f3\u8fb9\u7684\u5206\u6570\u4e3a 11\/4\uff0c\u5b83\u662f 63\/23 \u7684\u6700\u540e\u7b2c\u4e8c\u4e2a\u6e10\u8fd1\u5206\u6570\u3002\u7531\u4e8e 63 \u00d7 4 – 23 \u00d7 11 = -1\uff0c\u4e24\u8fb9\u5404\u4e58\u4ee5 7\uff0c\u79fb\u9879\u540e\u5c31\u5f9763 \u00d7 28+7 = 23 \u00d7 77\uff1b\u8fd9\u662f\u4e00\u4e2a\u7b54\u6848\u3002\u8fd9\u79cd\u6c42\u4e8c\u5143\u4e00\u6b21\u4e0d\u5b9a\u65b9\u7a0b\u5f0f ax+by=c \u7684\u65b9\u6cd5\uff0c\u662f\u7531 Aryabhata \u5f15\u5165\uff0c\u518d\u7531\u540e\u7ee7\u7684\u6570\u5b66\u5bb6\u6539\u8fdb\u7684\u3002\u8fd9\u79cd\u65b9\u7a0b\u5f0f\u82e5\u6709\u89e3\u7684\u8bdd\uff0c\u89e3\u6cd5\u7684\u8981\u70b9\u5728\u4e8e\u6c42 a\/b\uff08\u53ef\u5047\u8bbe a\uff0cb \u4e92\u8d28\uff09\u7684\u8fde\u5206\u6570\u5c55\u5f00\uff0c\u5f97\u6700\u540e\u7b2c\u4e8c\u4e2a\u6e10\u8fd1\u5206\u6570 q\/p\uff0c\u5219 \uff0c\u518d\u4e58\u4ee5\u9002\u5f53\u7684\u500d\u6570\u5c31\u597d\u4e86\u3002 <\/p>\n
\u9664\u4e86\u4e00\u6b21\u4e0d\u5b9a\u65b9\u7a0b\u5f0f\u5916\uff0c\u73b0\u5728\u4e16\u754c\u901a\u7528\u7684\u5370\u5ea6\u963f\u62c9\u4f2f\u6570\u5b57\u5728\u5176\u53d1\u6e90\u5730\u7684\u5386\u53f2\uff0c\u4e5f\u503c\u5f97\u505a\u6df1\u5165\u4e00\u70b9\u63a2\u8ba8\u3002 <\/p>\n
\u524d\u9762\u8bf4\u8fc7\uff0c\u5728\u897f\u5143\u524d\u4e94\u767e\u5e74\u4e4b\u524d\uff0c\u6709\u5173\u5370\u5ea6\u7684\u6587\u732e\u662f\u4e0d\u8db3\u7684\u3002\u56e0\u6b64\u6211\u4eec\u53ea\u80fd\u4ece\u540e\u6765\u7684\u6587\u732e\u63a8\u6d4b\u65e9\u671f\u5370\u5ea6\u4eba\u7684\u6570\u5b57\u89c2\u5ff5\u3002<\/p>\n
\u5370\u5ea6\u4eba\u5bf9\u62bd\u8c61\u7684\u6570\u76ee\u6709\u6240\u504f\u597d\uff0c\u4ed6\u4eec\u8ba4\u4e3a\u8981\u5c0a\u5d07\u795e\u53ea\u5723\u4eba\uff0c\u6700\u597d\u8d4b\u4e88\u4e00\u4e9b\u6570\u76ee\u3002\u5173\u4e8e\u4f5b\u7956\uff0c\u6709\u5982\u4e0b\u7684\u8bf4\u6cd5\uff1a\u201c\u4f5b\u7956\u670932\u79cd\u4e3b\u8981\u8c61\u5f81\u53ca80\u79cd\u6b21\u8981\u8c61\u5f81\u6765\u4ee3\u8868\u4ed6\uff1b\u4ed6\u7684\u6bcd\u4eb232\u79cd\uff0c\u4ed6\u8981\u51fa\u751f\u7684\u623f\u5b508\u79cd\u3002\u4ed6\u7684\u6bcd\u4eb2 Maya-Devi \u738b\u540e\u6709\u4e00\u767e\u4e07\u540d\u4f8d\u5973\u3002\u6210\u5343\u4e0a\u4e07\u7684\u5723\u8005\u667a\u8005\u4f1a\u6765\u671d\u4f5b\u3002\u4ed6\u7684\u738b\u5ea7\u662f\u82b1\u4e86\u6210\u4ebf\u4e2a Kalpas \u4e16\u4ee3\uff08\u4e00\u4e16\u4ee3\u4e3a43\u4ebf2\u5343\u4e07\u5e74\uff09\u7684\u7cbe\u5de5\u7ec6\u7422\u7684\u6210\u54c1\u3002\u5728\u5b55\u6210\u4f5b\u7956\u90a3\u665a\u7efd\u5f00\u4e86\u7684\u83b2\u82b1\uff0c\u5176\u82b1\u74e3\u4f38\u5c55\u52306\u53438\u767e\u4e07\u54e9\u4e4b\u5916\u3002\u201d <\/p>\n
\u5728\u8bb0\u8ff0\u4f5b\u7956\u884c\u8c0a\u7684\u300aLalitavistara\u300b\u4e2d\uff0c\u63d0\u53ca\u4f5b\u7956\u9752\u5e74\u65f6\uff0c\u4e3a\u4e86\u6c42\u5a5a\u800c\u5c55\u73b0\u7684\u6570\u6570\u624d\u80fd\u3002\u4ed6\u4e0d\u4f46\u80fd\u6570\u523010\u7684421\u6b21\u65b9\uff0c\u800c\u4e14\u4e5f\u80fd\u6570\u51fa\u4e09\u767e\u4e07\u4e2a\u4e16\u754c\u4e2d\u7684\u539f\u5b50\u603b\u65702 \u3002\u5728\u5370\u5ea6\u7684\u53e4\u5178\u6587\u5b66\u540d\u8457\u300aMahabharata\u300b\uff08Bharata \u5bab\u5ef7\u6545\u4e8b\uff09\u4e2d\uff0c\u4e5f\u65f6\u5e38\u63d0\u53ca\u53e4\u4ee3\u82f1\u96c4\u5728\u6570\u6570\u76ee\u65b9\u9762\u7684\u672c\u4e8b\u3002<\/p>\n
\u4e0d\u8bba\u8fd9\u4e9b\u6545\u4e8b\u7684\u771f\u5b9e\u6027\uff0c\u6211\u4eec\u53ef\u786e\u5b9a\u5b83\u4eec\u7684\u4f5c\u8005\u5bf9\u6570\u76ee\u90fd\u6709\u4e30\u5bcc\u7684\u60f3\u50cf\u529b\uff0c\u800c\u4e14\u5bf9\u5341\u8fdb\u4f4d\u4ee5\u53ca\u6570\u6570\u76ee\u53ef\u4ee5\u65e0\u7a77\u5ef6\u4f38\u7684\u539f\u7406\uff0c\u90fd\u6709\u4e86\u76f8\u5f53\u7684\u4e86\u89e3\u3002\u7136\u800c\u5728\u53e4\u4ee3\u7684\u68b5\u8bed\u4e2d\uff0c20\u300130\u3001\u2026\u2026\u300190\uff0c\u5728\u8fdb\u4f4d\u4f53\u7cfb\u672a\u6210\u719f\u524d\u5c31\u5df2\u51fa\u73b0\uff0c\u5176\u8bf4\u6cd5\u53ca\u7b26\u53f7\u4e0e\u4e2a\u4f4d\u6570\u7684\u6ca1\u6709\u7edd\u5bf9\u7684\u5173\u8054\uff0c\u8fd9\u662f\u4ece\u6709\u4f4d\u540d\u8fdb\u6b65\u5230\u65e0\u4f4d\u540d\u7684\u5341\u8fdb\u4f4d\u4f4d\u7f6e\u5b9a\u503c\u6cd5\u7684\u4e00\u4e2a\u969c\u788d\u3002\u4e00\u76f4\u5230\u897f\u5143\u516d\u767e\u5e74\u5de6\u53f3\uff0c\u4e5d\u4e2a\u4e2a\u4f4d\u6570\u5b57\u52a0\u4e0a\u4e00\u4e2a\u96f6\u5c31\u53ef\u4ee5\u8868\u793a\u4e00\u5207\u6570\u76ee\u7684\u60f3\u6cd5\uff0c\u624d\u8d8b\u4e8e\u6210\u719f\u3002 <\/p>\n
\u5370\u5ea6\u7684\u68b5\u6587\u65e9\u671f\u7528\u7684\u662f\u5a46\u7f57\u95e8\u6587\u5b57\uff0c\u56e0\u6b64\u6570\u5b57\u4e5f\u662f\u5a46\u7f57\u95e8\u3002\u5728\u4e5d\u4e16\u7eaa\u963f\u62c9\u4f2f\u4eba Alkwarizmi \u6b63\u5f0f\u5f15\u4ecb\u5230\u963f\u62c9\u4f2f\u4e4b\u524d\uff0c\u8fd9\u4e9b\u6570\u5b57\u5df2\u7ecf\u6709\u4e86\u4e00\u4e9b\u6f14\u53d8\uff0c\u5b83\u4eec\u53ef\u4ee5\u7528 Gvalior \u5e99\u5b87\u4e0a\u7684\u523b\u6587\u4e3a\u4ee3\u8868\u3002Gvalior \u6570\u5b57\u5728\u5370\u5ea6\u672c\u571f\u5219\u518d\u6b21\u6f14\u53d8\u6210 Devanagari \u6570\u5b57\uff08\u89c1\u56fe\u4e8c\uff09\u3002Devanagari \u662f\u4e00\u79cd\u5b57\u6bcd\uff0c\u73b0\u5728\u7684\u5370\u5ea6\u6587\u53ca\u76f8\u5173\u7684\u8bed\u7cfb\u90fd\u662f\u7528\u5176\u884d\u751f\u7684\u5b57\u6bcd\u7684\u3002Gvalior \u6570\u5b57\u4f20\u5230\u963f\u62c9\u4f2f\uff0c\u5176\u540e\u5206\u6210\u4e1c\u3001\u897f\u4e24\u652f\uff0c\u897f\u963f\u62c9\u4f2f\u6240\u7528\u7684\u6570\u5b57\u7ec8\u4e8e\u6f14\u53d8\u6210\u4eca\u65e5\u901a\u884c\u4e8e\u4e16\u754c\u7684\u963f\u62c9\u4f2f\u6570\u5b57\uff08\u89c1\u56fe\u4e09\uff09\u3002 <\/p>\n
\n\u56fe\u4e09\uff1a\u5370\u5ea6\u963f\u62c9\u4f2f\u6570\u5b57\u7684\u6f14\u53d8\u7cfb\u8c31 <\/p>\n
\u73b0\u5728\u7684\u5370\u5ea6\u5927\u4f53\u4e0a\u7528\u7684\u662f\u963f\u62c9\u4f2f\u6570\u5b57\uff0c\u800c\u53e4\u8001\u7684 Devanagari \u6570\u5b57\u867d\u7136\u5076\u800c\u7528\u53ca\uff0c\u4f46\u5176\u4e3b\u8981\u7684\u6d41\u884c\u5730\u533a\u662f\u5728\u5c3c\u6cca\u5c14\u7b49\u5730 3 \u3002 <\/p>\n
\uff08\u90e8\u5206\u56fe\u7247\u89c1\u539f\u6587\uff09<\/p>\n
http:\/\/episte.math.ntu.edu.tw\/articles\/sm\/sm_18_01_1\/index.html<\/p>\n","protected":false},"excerpt":{"rendered":"
\u66f9\u4eae\u5409\/\u53e4\u4ee3\u56db\u5927\u6587\u660e\u4e2d\uff0c\u4e2d\u56fd\u3001\u57c3\u53ca\u3001\u5df4\u6bd4\u4f26\u7684\u6570\u5b66\u53d1\u5c55\u8f83\u4e3a\u4eba\u6240\u719f\u6089\uff0c\u73b0\u5728\u6211\u4eec\u6765\u770b\u770b\u5370\u5ea6\uff1b\u7136\u800c\u8981\u8bfb\u5370\u5ea6\u7684\u6570\u5b66\uff0c\u6211\u4eec\u5fc5\u987b\u4e5f\u8981\u4e86\u89e3\u5370\u5ea6\u7684\u5386\u53f2\u3002 1920\u5e74\u4ee3\uff0c\u5728\u5370\u5ea6\u6cb3\u6d41\u57df\u53d1\u73b0\u4e86\u53e4\u4ee3\u7684\u9057\u8ff9\uff0c\u4f7f\u5370\u5ea6\u7684\u5386\u53f2\u53ef\u8ffd\u6eaf\u5230\u56db\u5343\u4e94\u767e\u5e74\u524d\u3002\u5176\u540e\u7684\u6316\u6398\u4f7f\u5730\u533a\u6269\u5f20\u5230\u73b0\u4eca\u5370\u5ea6\u7684\u897f\u5317\u90e8\u4e0e\u897f\u90e8\u3002\u5728\u8bf8\u591a\u7684\u9057\u8ff9\u4e2d\uff0c\u4f4d\u4e8e\u73b0\u5728\u5df4\u57fa\u65af\u5766\u5883\u5185\u7684 …
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