《周易時論合編．圖象幾表》的《易》數與數學：以〈極數概〉為核心

Numbers and Mathematics in the Zhouyi shilun hebian, tuxiang jibiao: A Preliminary Study of the ＂Jishu gai＂

李忠達(Lee Chung-ta)

《清華學報》 49卷3期 (2019/09) Pp. 399-436

https://doi.org/10.6503/THJCS.201909_49(3).0001

摘要

《周易時論合編．圖象幾表》收錄天文、曆算、聲律、醫藥、物理、算數的知識，反映出中國古代科學家、數學家以《周易》為一切自然原理之基礎的信念。作為「內算」的數學，可以發揮通神明、順性命的大用；而作為「外算」的數學，也有經世務、類萬物的應用價值。數學之所以具有如此崇高的功能，是因為它根源於《周易》，因此受到《周易》形上之理的滲透，並分享了《易》數能預卜未來的神祕力量。《圖象幾表》在繪製與解說《易》圖時，在《河圖》、《洛書》等象數學中融入大量數學的內容，突顯出中國古代《易》學與數學並未歧而為二的思維模式。

關鍵字

《周易時論合編》 ； 《圖象幾表》 ； 數學 ； 象數 ； 內算外算

並列摘要

The Zhouyi shilun hebian 周易時論合編, compiled in the mid-seventeenth century, collected together large amounts of earlier research on astronomy, musicology, medicine, physics and mathematics. The text not only reveals the Chinese interest in natural science, but also the belief among Chinese mathematicians and scientists that the Zhouyi 周易 had perfectly rendered visible Nature's truth. The study of numbers in China was perceived to have had two functions: an inner-calculation (neisuan 內算), which concerned both the ability to be numinous and illuminating (shenming 神明) and to comply with one's Nature and Destiny (xingming 性命); and an outer-calculation (waisuan 外算), which dealt with practical problems involving the application of certain mathematical methods. The idea that both inner and outer calculations, two subsets of numerical learning, originated with the Zhouyi inspired Chinese mathematicians to study the metaphysics of the Zhouyi and its numerology, which since antiquity was thought to have held the keys to predicting the future. In depicting and interpreting Zhouyi images, the Tuxiang jibiao 圖象幾表, found at the beginning of the Zhouyi shilun hebian, made use of traditional mathematical knowledge and the image-number symbolism of the Zhouyi to express a combined worldview that did not treat natural sciences and numerology as distinct systems of thought.

並列關鍵字

Zhouyi shilun hebian 周易時論合編 ； Tuxiang jibiao 圖象幾表 ； mathematics ； image-number symbolism ； inner calculation and outer calculation

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