Lì zhì 歷誌
Calendar Treatise by anonymous
About the work
The Lì zhì 歷誌, in fifteen juàn, is an anonymous late-Míng treatise that — despite the generic-sounding title, which would seem to promise a chronological “calendar treatise” — is in substance a textbook of plane and spherical trigonometry adapted to astronomical computation. It opens by asserting that “trigonometry is the ridgepole of calendrical computation” (sānjiǎofǎ wéi lìsuàn zhī gāng 三角法為曆算之綱; the source has 二角法, evidently a graphic slip for 三角法), arguing that the inherited jiǔzhāng 九章 methods can handle straight lines and plane figures but that celestial computation requires both rectilinear (zhíxiàn sānjiǎo 直線三角) and curvilinear/spherical (qūxiàn sānjiǎo 曲線三角) trigonometry.
Abstract
The work has no preface, dedication, or attribution. It opens directly with definitions in the manner of the late-Míng / early-Qīng Jesuit-mediated mathematical works: points (diǎn 㸃 — “that which has no parts” 無分), lines, planes, and the angle taxonomy (zhèngjiǎo 正角 / right angle, dùnjiǎo 鈍角 / obtuse angle, ruìjiǎo 銳角 / acute angle), with edges classified as equal, larger, or smaller (děng/dà/xiǎo 等大小). The vocabulary (gōngjiè 公界 for boundary, diǎn zhě wú fēn 㸃者無分 for the Euclidean-style definition of a point, ruìjiǎo / dùnjiǎo for acute/obtuse angles), and the framing argument that “to engage in calendrical study one must from the outset work with the plane rectilinear forms” (治曆者必從事于平面直線形), place this work unambiguously in the post-Chóngzhēn lìshū 崇禎曆書 lineage — that is, in the milieu of Xú Guāngqǐ 徐光啟, Lǐ Tiānjīng 李天經, and the Jesuit collaborators (Schall, Rho) responsible for the Cèliáng quányì 測量全義 and the rest of the Chóngzhēn lìshū compilation of 1631–35.
In all probability the Lì zhì is either a section excerpted from the Chóngzhēn lìshū corpus, or a derivative pedagogical recasting of its trigonometric chapters intended for circulation in the late-Míng provincial market. NotBefore is set at 1631 (the first instalment-presentation of the Chóngzhēn lìshū); notAfter at 1644 (the fall of the Míng), within which window an anonymous derivative is most plausibly placed. The author’s silence and the work’s anonymous transmission are typical of the dispersed reception of the Chóngzhēn lìshū materials by provincial calendrical practitioners who did not have direct access to the imperial compilation but reproduced its mathematical core for technical use.
Translations and research
- Hashimoto Keizō 橋本敬造. 1988. Hsü Kuang-ch’i and Astronomical Reform: The Process of the Chinese Acceptance of Western Astronomy 1629–1635. Suita: Kansai University Press. — The standard study of the Chóng-zhēn lì-shū compilation.
- Jami, Catherine. 2012. The Emperor’s New Mathematics: Western Learning and Imperial Authority during the Kangxi Reign (1662–1722). Oxford: Oxford University Press. — Continues the Chóng-zhēn story into the Kāng-xī era.
- Engelfriet, Peter M. 1998. Euclid in China: The Genesis of the First Translation of Euclid’s Elements. Leiden: Brill. — Treats the trigonometric and Euclidean-style vocabulary into which works such as the present anonymous Lì zhì fit.
Links
- Parent compilation: the Chóngzhēn lìshū 崇禎曆書, surviving as KR3f0013 Xīyáng xīnfǎ suànshū 西洋新法算書 in the present catalog.
- Cognate trigonometric chapter of the parent: Cèliáng quányì 測量全義.