中国早期青铜技术中的几何作图法
|
摘要
汉代画像石和唐墓出土彩帛皆出现过圆规、直角尺等测绘工具的图像,其使用方式以往鲜有研究。现存历代文献包括算经中,并没有使用规、矩进行几何作图的记载。因此,通常认为,中国古代数学都是具体问题的演算细草,没有抽象的数学方法,没有形成一套科学完整的几何作图体系,明末徐光启翻译《几何原本》,才将古希腊的尺规作图等欧氏几何学内容传入中国。本文介绍并分析了考古资料中所见东周到汉代一些出土实物上的现象所反映出的一些几何绘图方法,包括侯马铸铜遗址出土东周模、范和型芯上的几何作图求圆心痕迹,方壶陶模上的弧线画法及汉代铜鼓鼓面上呈螺线状排列的雷纹装饰的参考线画法。这些资料说明,至迟在东周时代,铸工已经运用了一些成熟的几何作图法。对早期手工业遗物的观察可以为数学史研究提供新的途径,弥补早期几何学知识在文献上的缺失,以便对我国古代数学发展水平有更为客观的认识。
Although the image drawn by means of the compasses and try square had been found in the stone carvings of the Han dynasty and on the silk paintings excavated from the Tang dynasty, there are few historical documents in researching the using method of these measure and drawing tools in geometrical drawing. Therefore, it is always believed that there was only arithmetic to concrete problems without abstract method or scientific geometrical drawing system in ancient Chinese mathematics. The ancient Greek geometry including the drawing with compasses and try squares hadn't been introduced to China until Xu Guangqi translated Euclid's Elements in the late Ming dynasty. The paper makes an analysis on the geometrical drawing methods according to some objects unearthed from the Eastern Zhou bronze foundry site in Houma, such as finding the center of a circle in the core of molds, clay models and sectional molds. The arc on the pottery mold of rectangular hu, the reference lines of the spiral thunder pattern on the bronze drum of the Han dynasty unearthed from Guangxi were also drawn in the similar method. According these materials, it can be confirmed that the ancient caster had already applied the geometrical drawing method in the Eastern Zhou dynasty at the latest. The research on relics of the ancient handicraft industry can provide a new approach for the study on the history of ancient Chinese mathematics to make up for the lack of the literature of early geometry and carry out a more objective evaluation on the development of ancient Chinese mathematics.
Although the image drawn by means of the compasses and try square had been found in the stone carvings of the Han dynasty and on the silk paintings excavated from the Tang dynasty, there are few historical documents in researching the using method of these measure and drawing tools in geometrical drawing. Therefore, it is always believed that there was only arithmetic to concrete problems without abstract method or scientific geometrical drawing system in ancient Chinese mathematics. The ancient Greek geometry including the drawing with compasses and try squares hadn't been introduced to China until Xu Guangqi translated Euclid's Elements in the late Ming dynasty. The paper makes an analysis on the geometrical drawing methods according to some objects unearthed from the Eastern Zhou bronze foundry site in Houma, such as finding the center of a circle in the core of molds, clay models and sectional molds. The arc on the pottery mold of rectangular hu, the reference lines of the spiral thunder pattern on the bronze drum of the Han dynasty unearthed from Guangxi were also drawn in the similar method. According these materials, it can be confirmed that the ancient caster had already applied the geometrical drawing method in the Eastern Zhou dynasty at the latest. The research on relics of the ancient handicraft industry can provide a new approach for the study on the history of ancient Chinese mathematics to make up for the lack of the literature of early geometry and carry out a more objective evaluation on the development of ancient Chinese mathematics.
引文
[1]中国画像石全集编辑委员会编《中国美术分类全集·中国画像石全集1·山东画像石》,山东美术出版社,2000年,图版八〇。
[2]山西省考古研究所:《侯马铸铜遗址》,文物出版社,1993年,第152-153页。
[3]同[2],第291-292页。
[4]闻人军译注《考工记》,上海古籍出版社,2008年,第20-21、55-56页。
[5]同[2],288-289页。
[6]刘彦琪、朱丽彬等:《广西桂平市博物馆馆藏北流型铜鼓的印轮滚印技术》,《广西民族大学学报》(自然科学版)2018年第3期。
[7]浙江省文物考古研究所:《瑶山》,文物出版社,2003年,彩图493。
[8]刘云辉:《陕西出土东周玉器》,文物出版社、台湾众志美术出版社,2006年,第148-150页。
[9]南京博物院:《鸿山越墓出土玉器》,文物出版社,2007年,图版22。
[10]《南越王墓玉器》,广州西汉南越王墓博物馆、香港中文大学文物馆、求知雅集、两木出版社出版,1991年,图版133、156、157。青铜器研究Br o n z e St众志
[2]山西省考古研究所:《侯马铸铜遗址》,文物出版社,1993年,第152-153页。
[3]同[2],第291-292页。
[4]闻人军译注《考工记》,上海古籍出版社,2008年,第20-21、55-56页。
[5]同[2],288-289页。
[6]刘彦琪、朱丽彬等:《广西桂平市博物馆馆藏北流型铜鼓的印轮滚印技术》,《广西民族大学学报》(自然科学版)2018年第3期。
[7]浙江省文物考古研究所:《瑶山》,文物出版社,2003年,彩图493。
[8]刘云辉:《陕西出土东周玉器》,文物出版社、台湾众志美术出版社,2006年,第148-150页。
[9]南京博物院:《鸿山越墓出土玉器》,文物出版社,2007年,图版22。
[10]《南越王墓玉器》,广州西汉南越王墓博物馆、香港中文大学文物馆、求知雅集、两木出版社出版,1991年,图版133、156、157。青铜器研究Br o n z e St众志