十二、十三世纪,北方出现了很多天元书的作品,大部分都失传了 。最早流传下来的以天元术为主要方法的作品是李烨的《量圆海镜》十二卷(公元1248年)和三卷《一古言段》(公元1259年) 。李烨(公元1192-1279),字任卿,别号景斋,栾城(今河北省)镇定人,大兴(今北京)人 。他的父亲是一位清正廉洁的官员 。李烨从小受过良好的教育,热爱数学 。年少时成为中原著名学者 。进入元朝后,他隐居在辛郭(guo Guo)一带(今山西省北部),在极其艰苦的条件下学习数学和各种研究 。他一生写了很多文史,只有《景斋古今》 。《量海镜》在东元九容的基础上,考虑了毕达哥拉斯形与圆的10个基本关系 。长问题,答案当然是一样的 。这些问题大部分都需要使用天元书来列出方程 。第一卷是全书的理论基础,包括循环城市图式、标识杂记等部分 。用天、地、干、坤等汉字来表示圆城图式中的点,是一项创举 。辨认杂记共提出692个公式,除8个外均正确 。《一古言段》第64题,这是一部运用天元法解译姜舟(可能是北宋)《易古集》中的方程式的作品 。其中,保存了《易古集》的若干题名和旧技(法) 。
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