九章算术注序（刘徽）
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昔在庖犠氏始画八卦，以通神明之德，以类万物之情，作九九之数，以合六
爻之变。龙腾小说网ltxsba.com暨于黄帝神而化之，引而伸之，于是建历纪，协律吕，用稽道原，然后
两仪四象精微之气可得而效焉。记称隶首作数，其详未之闻也。按周公制礼而有
九数，九数之流，则《九章》是矣。往者暴秦焚书，经术散坏。自时厥后，汉北
平侯张苍、大司农中丞耿寿昌皆以善算命世。苍等因旧文之遗残，各称删补。故
校其目则与古或异，而所论者多近语也。徽幼习《九章》，长再详览。观阴阳之
割裂，总算术之根源，探赜之暇，遂悟其意。是以敢竭顽鲁，采其所见，为之作
注。事类相推，各有攸归，故枝条虽分而同本榦知，发其一端而已。又所析理以
辞，解体用图，庶亦约而能周，通而不黩，览之者思过半矣。且算在六艺，古者
以宾兴贤能，教习国子；虽曰九数，其能穷纤入微，探测无方；至于以法相传，
亦犹规矩度量可得而共，非特难为也。当今好之者寡，故世虽多通才达学，而未
必能综于此耳。《周官·大司徒》职，夏至日中立八尺之表。其景尺有五寸，谓
之地中。说云，南戴日下万五千里。夫云尔者，以术推之。案：《九章》立四表
望远及因木望山之术，皆端旁互见，无有超邈若斯之类。然则苍等为术犹未足以
博尽群数也。徽寻九数有重差之名，原其指趣乃所以施于此也。凡望极高、测绝
深而兼知其远者必用重差、句股，则必以重差为率，故曰重差也。立两表于洛阳
之城，令高八尺，南北各尽平地。同日度其正中之时。以景差为法，表高乘表间
为实，实如法而一。所得加表高，即日去地也。以南表之景乘表间为实，实如法
而一，即为从南表至南戴日下也。以南戴日下及日去地为句、股，为之求弦，即
日去人也。以径寸之筒南望日，日满筒空，则定筒之长短以为股率，以筒径为句
率，日去人之数为大股，大股之句即日径也。虽夫圆穹之象犹曰可度，又况泰山
之高与江海之广哉。徽以为今之史籍且略举天地之物，考论厥数，载之于志，以
阐世术之美，辄造《重差》，并为注解，以究古人之意，缀于句股之下。度高者
重表，测深者累矩，孤离者三望，离而又旁求者四望。触类而长之，则虽幽遐诡
伏，靡所不入，博物君子，详而览焉。
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