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尺算日晷新義

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Text ID
KR3fc063
Date
1800–1841
Dynasty
清

Chǐsuàn rìguǐ xīnyì 尺算日晷新義

New Discussion of the Sliding-Rod-Computed Sundial by 劉衡 (撰)

About the work

劉衡 Liú Héng’s (1776–1841) treatise in 3 juàn on the chǐsuàn rìguǐ 尺算日晷 — a sundial whose hour-and-azimuth markings can be calculated and laid out with the chǐsuàn 尺算 sliding-rod (the Chinese version of the European sector or proportional compass, introduced to China in the seventeenth century via the Jesuit mathematical translations and refined under 梅文鼎 Méi Wéndǐng).

Abstract

The chǐsuàn 尺算 (sliding-rod calculator, equivalent to the European sector or proportional compass) is a graduated mechanical instrument with two hinged legs marked in arithmetic and trigonometric scales. Set to a given angle, the instrument permits rapid graphical computation of proportions, trigonometric values, and similar quantities. The instrument was introduced to China by the Jesuit mathematicians in the early seventeenth century and elaborated by 梅文鼎 Méi Wéndǐng (whose Chǐsuàn 尺算 treatise is the principal early Chinese exposition).

The rìguǐ 日晷 (sundial) requires precise laying-out of hour-lines on a plane (whether horizontal, equatorial, or arbitrary) such that the shadow of the gnomon falls on the correct hour-line at each hour of the day, accounting for the latitude of the place and the declination of the sun. The laying-out reduces to a sequence of trigonometric computations — the natural application domain of the chǐsuàn.

劉衡 Liú Héng’s 3-juàn treatise presents the systematic theory of laying-out sundial markings using the chǐsuàn. The first juàn presents the basic computation; the second extends to non-horizontal dial-faces; the third addresses the supplementary computations (the equation of time, the variable solar declination across the year, etc.) needed for high-accuracy sundial work. The title’s xīnyì 新義 (“new discussion”) indicates that the treatise is presented as Liú Héng’s own systematic working of the problem rather than an exposition of an existing tradition.

The work is the fullest mid-Qīng treatment of the chǐsuàn application to sundial-design and one of the principal Qīng works on practical horology generally. It belongs to the broader nineteenth-century interest in practical instrument-mathematics that also produced Liú Héng’s surveying treatise KR3fc064.

Dating: Liú Héng lived 1776–1841. notBefore 1800; notAfter 1841.

Translations and research

  • Engelfriet, Peter M. 1998. Euclid in China. Leiden: Brill. — Treats the Jesuit translations including the chǐ-suàn / sector tradition.
  • Jami, Catherine. 2012. The Emperor’s New Mathematics. Oxford: Oxford University Press.
  • Wáng Pīng 王萍. 1972. Xī-fāng lì-suàn-xué zhī shū-rù 西方曆算學之輸入. Tái-běi: Zhōng-yāng yán-jiū-yuàn jìn-dài-shǐ yán-jiū-suǒ.

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