chung asked in 文學及人文學歷史 · 1 decade ago

# 歐幾里得(Euclid)的生平事跡?

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Euclid (Greek: Εὐκλείδης — Eukleidēs), fl. 300 BC, also known as Euclid of Alexandria, &quot;The Father of Geometry&quot; was a Greek mathematician of the Hellenistic period who flourished in Alexandria, Egypt, almost certainly during the reign of Ptolemy I (323 BC–283 BC). His Elements is the most successful textbook in the history of mathematics. In it, the principles of Euclidean geometry are deduced from a small set of axioms. Euclid&#39;s method of proving mathematical theorems by logical deduction from accepted principles remains the backbone of all mathematics, imbuing that field with its characteristic rigor.

Euclid also wrote works on perspective, conic sections, spherical geometry, and possibly quadric surfaces.

Biographical knowledge：

Little is known about Euclid other than his writings. What little biographical information we do have comes largely from commentaries by Proclus and Pappus of Alexandria: Euclid was active at the great Library of Alexandria and may have studied at Plato&#39;s Academy in Greece. Euclid&#39;s exact lifespan and place of birth are unknown.

Some writers in the Middle Ages confused him with Euclid of Megara, a Greek Socratic philosopher who lived approximately one century earlier.

The Elements：

Although many of the results in Elements originated with earlier mathematicians, one of Euclid&#39;s accomplishments was to present them in a single, logically coherent framework, making it easy to use and easy to reference, including a system of rigorous mathematical proofs that remains the basis of mathematics 23 centuries later.

Although best-known for its geometric results, the Elements also includes number theory. It considers the connection between perfect numbers and Mersenne primes, the infinitude of prime numbers, Euclid&#39;s lemma on factorization (which leads to the fundamental theorem of arithmetic on uniqueness of prime factorizations), and the Euclidean algorithm for finding the greatest common divisor of two numbers.

The geometrical system described in the Elements was long known simply as geometry, and was considered to be the only geometry possible. Today, however, that system is often referred to as Euclidean geometry to distinguish it from other so-called Non-Euclidean geometries that mathematicians discovered in the 19th century.

• 1 decade ago

歐幾里得（Euclid）是公元前300年左右的希臘數學家，以其所著的《幾何原本》（Elements）聞名於世。對於他的生平，現在知道的很少。他生活的年代，是根據下列的記載來確定的。普羅克洛斯（Proclus）是雅典柏拉圖學園晚期的導師，公元450年左右，他給《幾何原本》作注，寫了一個簡明的《幾何學發展概要》，字數雖不多，但已包括從泰勒斯（Thales）到歐幾里得數百年間主要數學家的事跡，這幾何學史的重要資料。這本《幾何學發展概要》中指出，歐幾里得是托勒密一世時代的人，早年學於雅典，深知柏拉圖（Plato）的學說。又說阿基米德（Archimedes）的書引用過《幾何原本》的命題，可見他早於阿基米德。另一位學者帕波斯（Pappus）在《數學編》中提到阿波羅尼奧斯（Apollonius）長期住在亞歷山大，和歐幾里得的學生在一起。這說明歐幾里得曾在亞歷山大教過學。

《幾何學發展概要》還記述了這樣一則故事：托勒密王問歐幾里得說，除了他的《幾何原本》之外，還有沒有其他學習幾何的捷徑。歐幾里得回答道：「在幾何裏，沒有專為國王鋪設的大道」。這句話成為傳誦千古的學習箴言。斯托比亞斯（Stobaeus）記述另一則故事，一個學生才開始學習第一個命題，就問學了幾何學之後將得到些甚麼。歐幾里得說：「給他三個錢幣，因為他想學習中獲利。」由此可知歐幾里得主張學習必須循序漸進、刻苦鑽研，不贊成投機取巧的作風也反對狹隘實用觀點。帕波斯特別讚賞歐幾里得的謙遜，他從不掠人之美，也沒有聲稱過哪些是自己的獨創。而阿波羅尼奧斯則不然，他過分突出自己，明明是歐幾里得研究過的工作，他在《圓錐曲線論》（Conics）中也沒有歸功於歐幾里得。

除了《幾何原本》之外，歐幾里得還有不少著作，可惜大都失傳。唯一保存下來的純粹幾何著作《己知數》（The data），體例和《幾何原本》前6卷相似，包括94個命題，指出若圖形中的某些元素己知，則另外的一些元素也可以確定。《圓形的分割》（On divisions of figures）現存拉丁文本與阿拉伯文本，論述用直線將已知圖形分為相等的部分或成比例的部分。《光學》（Optica）是早期的幾何光學著作之一，研究透視問題，指出光的入射角等於反射角。認為視學是眼睛發出光線到達物體的結果等。還有一些著作未能確定是否屬於歐幾里得，而且已經散失。

Source(s): 藍紀正、朱恩寬譯，《歐幾里得幾何原本》，九章出版社，台灣，1992