《圜锥曲线说》为李善兰独创，韦烈亚力当年就做了证

最初版出现于咸丰九年（1859）墨海书馆原刻本，当年依附于《重学》二十卷末尾，作为附录三卷出现的，没单独成册。以区别正本“口译”。馆藏：上海图书馆、大英博物馆、阿姆斯特丹国际社会史研究所藏原刊本。1867年后来又李善兰又单独出过四版。

伟烈亚力1867关于中国数学的论文，对1859年附录版李善兰的独造，给予了肯定：The three-volume supplement on conic curves attached to Chung-hsüeh cannot be regarded as a translated copy of any Western monograph. Joseph Edkins merely furnished fragmentary verbal notes of scattered geometric propositions; there exists no complete Western text matching Li’s full chapter division, deductive sequence, native terminology and vertical illustrative diagrams.Allification of ellipse, parabola, hyperbola, all original Chinese names for focus, axis, asymptote, tangent, all geometric demonstrations adjusted to Chinese ancient proportional algorithm, every drawing and textual layout are the exclusive independent work of Li Shanlan.This supplementary mathematical treatise is indispensable for comprehending orbital motion and curved-surface calculation in the mechanical text, yet its entire theoretical framework was built by Li relying on his own mastery of tian-yuan and duoji series, long before he received any Western mathematical materials. The missionary’s oral hints are merely trivial auxiliary references, not the foundation of the whole work.直译附于《重学》后的三卷圆锥曲线附篇，不可视作任何西洋专著的译本。艾约瑟（重学正文口译者——笔者注）仅零散口头转述若干碎片化几何命题；不存在任何完整西文典籍，能对应李善兰完整分卷、推演次序、自创汉文术语、适配竖排的整套附图。椭圆、抛物线、双曲线全部分类体系，焦点、轴线、渐近线、切线全套原创汉文名词，所有贴合中国传统比例算法重构的几何证明，全部绘图与文本编排，皆为李善兰一人独立完成。这份数学附录是读懂力学典籍里轨道、曲面演算的必备基础，但全书整套理论框架，是李善兰凭借自身早已精通的天元、垛积术搭建而成，远在接触任何西洋数学材料之前便已具备功底。传教士口头提点的零星内容，只是微不足道的辅助参考，绝非全书根基。

其实，圆锥曲线理论，必须以几何、坐标系与解析几何、天文学为基础。