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-> 測圓海鏡

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RelationTargetTextual basis
creatorperson:李冶四庫全書總目提要·卷107 子部·天文算法類二》:元李冶撰。
indexed-inwork:四庫全書總目提要四庫全書總目提要·卷107 子部·天文算法類二》:《測圓海鏡》十二卷{{編修李潢家藏本}}
    juan-size 12四庫全書總目提要·卷107 子部·天文算法類二》:《測圓海鏡》十二卷{{編修李潢家藏本}}
    stated-category 天文算法
    stated-subcategory 算書
    juan-size 12
    stated-category 天文算法
    stated-subcategory 算書
Ceyuan haijing (測圓海鏡 cè yuán hǎi jìng, literally sea mirror of circle measurements) is a treatise on solving geometry problems with the algebra of Tian yuan shu written by the mathematician Li Zhi in 1248 in the time of the Mongol Empire. It is a collection of 692 formula and 170 problems, all derived from the same master diagram of a round town inscribed in a right triangle and a square. They often involve two people who walk on straight lines until they can see each other, meet or reach a tree or pagoda in a certain spot. It is an algebraic geometry book, the purpose of book is to study intricated geometrical relations by algebra.

Majority of the geometry problems are solved by polynomial equations, which are represented using a method called tian yuan shu, "coefficient array method" or literally "method of the celestial unknown". Li Zhi is the earliest extant source of this method, though it was known before him in some form. It is a positional system of rod numerals to represent polynomial equations.

Ceyuan haijing was first introduced to the west by the British Protestant Christian missionary to China, Alexander Wylie in his book Notes on Chinese Literature, 1902. He wrote:

This treatise consists of 12 volumes.

Read more...: Volume 1   Diagram of a Round Town   Triangles and their sides   Length of Line Segments   Segment numbers   Definitions and formula   Miscellaneous formula   The Five Sums and The Five Differences   Volume 2  

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Read more...: 內容   卷一   圓城圖式   總率名號   今問正數   識別雜記   名目   雜用公式   五和五較   新設第一率   新設第二率   新設第三率   新設第四率   第二卷  

The text above has been excerpted automatically from Wikipedia - please correct any errors in the original article.


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