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題 名 | 再論劉徽關於陽馬與羨除公式的證明=On Ancient Chinese Derivation of the Volumes of a Pyramid and a Cuneate Solid |
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作 者 | 曲安京; | 書刊名 | 清華學報 |
卷 期 | 27:2 1997.06[民86.06] |
頁 次 | 頁201-215 |
分類號 | 310.92 |
關鍵詞 | 劉徽; 陽馬; 羨除; 多面體; Liu Hui; Volume of pyramid; Volume of cuneate solid; Polyhedron; |
語 文 | 中文(Chinese) |
中文摘要 | 陽馬術是中國古代體積理論的基石之一,人們對劉徽之論證的理解仍存在分歧 和疑問,在對原文只進行了一個字(只誤為尺)校改的前提下,克服了現存的矛盾。以往對 羨除術的研究,失之於對羨除的分類太細,從而誤判劉徽的證明有漏洞。事實上,劉徽的 證明完整無缺,其思路簡潔明快。 |
英文摘要 | The theory of polyhedron volume in ancient Chinese mathematics was based on yangma shu, the volume of a pyramid. Yanchu shu, the volume of a cuneate solid, did not exist in Euclid's Elements. The derivation of yangma shu and yanchu shu in Liu Hui's commentary on the Nine Chapters on Mathematical Art has been studied by scholars in and out China. In order to under-standing the meaning of yangma shu, several key words in orinial text have been changed in different ways. In fact, only one word was misprinted in Liu Hui's commentary on yangma shu. It has been considered that the proof of yanchu shu in Liu Hui's commentary is not perfect. The reexamination on yanchu shu shows that Liu Hui's proof is much concise than the understanding of those who divided a yanchu into many cases, and then found that some cases Liu Hui did not give proofs. The reasult is that Liu Hui's proof on yanchu shu is complete. |
本系統中英文摘要資訊取自各篇刊載內容。