歷代三寶紀 12.106

12.106

右一部一卷。翻經學士涇陽劉憑撰。憑內外學數術偏工。每以前代翻經算數比校術法頗有不同。故為斯演。其序略云。世之道藝有淺有深。人之稟學有疎有密。故尋算之用也則兼該大衍。其不思也則致惑三隅。然華夏數法自有三等之差。天竺所陳何無異端之例。然先譯經並以大千稱為百億。言一由旬為四十里。依諸算計悉不相合。竊疑翻傳之日彼此異音。指麾之際於斯取失。故錄眾經算數之法。與華夏相參。十十變之傍通對衍。庶擬翻譯之次執而辯惑。既參經語故此錄云。

The above one work is in one fascicle. Written by Liu Ping of Jingyang, a Translation Scholar. Ping was versed in both inner and outer learning, and was especially skilled in mathematical arts. Because the calculation methods and comparative techniques used in translating scriptures in previous eras differed considerably, he composed this exposition. His preface states in brief: 'The arts and skills of the world have their shallow and deep; what people receive in learning has its coarse and refined. Thus, when the application of calculation is explored, it embraces the Great Expansion; when people do not reflect upon it, they fall into perplexity over the three corners. Now, the numerical methods of China naturally have three gradations of difference; how could what is set forth in Tianzhu lack instances of divergence? Yet earlier translations of scriptures all rendered the great chiliocosm as "ten billion" (baiyi) and stated that one yojana is forty li; according to various mathematical calculations, these do not tally at all. I suspect that at the time of translation, the sounds on both sides differed, and during the instruction, errors were made here. Therefore, I have recorded the calculation methods of the various scriptures, comparing them with those of China, transforming them by tens and cross-referencing and developing them, in the hope that when translating, one may grasp this to resolve perplexities. Since it relates to the words of the scriptures, it is recorded here.'