Thales of Miletus（米利都的泰勒斯）4
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2023-11-25 21:20
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文献来源：MacTutor 数学历史档案-Thales of Miletus作者 | 由JJ O'Connor 和 EF Robertson撰写 最后更新于 1999 年 1 月
After the eclipse on 28 May, 585 BC Herodotus wrote:-.... day was all of a sudden changed into night. This event had been foretold by Thales, the Milesian, who forewarned the Ionians of it, fixing for it the very year in which it took place. The Medes and Lydians, when they observed the change, ceased fighting, and were alike anxious to have terms of peace agreed on....白天突然变成了黑夜。这一事件由米利安人泰勒斯预言过，他预先警告了爱奥尼亚人，并确定了它发生的确切年份。当米底人和吕底亚人观察到这种变化时，他们停止了战斗，并且都渴望达成和平协议。Longrigg in even doubts that Thales predicted the eclipse by guessing, writing:-... a more likely explanation seems to be simply that Thales happened to be the savant around at the time when this striking astronomical phenomenon occurred and the assumption was made that as a savant he must have been able to predict it....更有可能的解释似乎仅是塞勒斯恰好是在这一引人注目的天文现象发生时的学者，因此人们假设他作为一位学者必定能够预测到这一事件。There are several accounts of how Thales measured the height of pyramids. Diogenes Laertius writing in the second century AD quotes Hieronymus, a pupil of Aristotle :-关于泰勒兹如何测量金字塔的高度，有几种说法。公元二世纪的第欧根尼·拉尔提乌斯（Diogenes Laertius）引用了亚里士多德的学生希罗尼穆斯（Hieronymus）的话：Hieronymus says that [Thales] even succeeded in measuring the pyramids by observation of the length of their shadow at the moment when our shadows are equal to our own height.希罗尼穆斯说（Hieronymus）表示，[泰勒斯]甚至成功通过观察金字塔在我们的影子等于我们自己身高的瞬间的长度来进行测量。This appears to contain no subtle geometrical knowledge, merely an empirical observation that at the instant when the length of the shadow of one object coincides with its height, then the same will be true for all other objects. A similar statement is made by Pliny :-这似乎不包含任何微妙的几何知识，而只是一种经验观察，即当一个物体的阴影长度与其高度重合时，所有其他物体也是如此。普林尼也作了类似的声明：Thales discovered how to obtain the height of pyramids and all other similar objects, namely, by measuring the shadow of the object at the time when a body and its shadow are equal in length.
泰勒斯发现了如何获得金字塔和所有其他类似物体的高度，即通过在物体及其影子相等长度的时刻测量物体的影子。Plutarch however recounts the story in a form which, if accurate, would mean that Thales was getting close to the idea of similar triangles:-然而，普鲁塔克（Plutarch）以一种形式叙述了这个故事，如果属实，那就意味着塞勒斯接近了类似三角形的概念：... without trouble or the assistance of any instrument [he] merely set up a stick at the extremity of the shadow cast by the pyramid and, having thus made two triangles by the impact of the sun's rays, ... showed that the pyramid has to the stick the same ratio which the shadow [of the pyramid] has to the shadow [of the stick]...毫不费力，也不借助任何仪器的帮助，[他]只是在金字塔投射的影子的末端竖起一根棍子，通过太阳光线的影响构成了两个三角形，...表明金字塔与棍子的比例与[金字塔]的影子与[棍子]的影子的比例相同。Of course Thales could have used these geometrical methods for solving practical problems, having merely observed the properties and having no appreciation of what it means to prove a geometrical theorem. This is in line with the views of Russell who writes of Thales contributions to mathematics in [12]:-当然，泰勒斯本可以使用这些几何方法来解决实际问题，但他只是观察了其性质，而没有意识到证明几何定理意味着什么。这与罗素的观点一致，他在[12]中写到泰勒斯对数学的贡献：Thales is said to have travelled in Egypt, and to have thence brought to the Greeks the science of geometry. What Egyptians knew of geometry was mainly rules of thumb, and there is no reason to believe that Thales arrived at deductive proofs, such as later Greeks discovered.据称泰勒斯曾在埃及旅行，随后向希腊人介绍了几何学的科学。埃及人对几何学的认识主要是经验性的规则，并没有理由相信塞勒斯能够达到后来希腊人所发展出的演绎证明的水平。
On the other hand B L van der Waerden [16] claims that Thales put geometry on a logical footing and was well aware of the notion of proving a geometrical theorem. However, although there is much evidence to suggest that Thales made some fundamental contributions to geometry, it is easy to interpret his contributions in the light of our own knowledge, thereby believing that Thales had a fuller appreciation of geometry than he could possibly have achieved. In many textbooks on the history of mathematics Thales is credited with five theorems of elementary geometry:-
- A circle is bisected by any diameter.
- The base angles of an isosceles triangle are equal.
- The angles between two intersecting straight lines are equal.
- Two triangles are congruent if they have two angles and one side equal.
- An angle in a semicircle is a right angle.
另一方面，B.L.范德瓦尔登（B.L. van der Waerden）[16]声称泰勒斯将几何学建立在逻辑基础上，并清楚地意识到证明几何定理的概念。然而，尽管有许多证据表明泰勒斯在几何学方面做出了一些基础性的贡献，但很容易根据我们自己的知识解释他的贡献，从而认为泰勒斯对几何学的理解比他实际上可能达到的要更充分。在许多关于数学历史的教科书中，塞勒斯被归功于五个基本几何定理：4. 如果两个三角形有两个角和一边相等，则它们全等。What is the basis for these claims? Proclus, writing around 450 AD, is the basis for the first four of these claims, in the third and fourth cases quoting the work History of Geometry by Eudemus of Rhodes, who was a pupil of Aristotle, as his source. The History of Geometry by Eudemus is now lost but there is no reason to doubt Proclus. The fifth theorem is believed to be due to Thales because of a passage from Diogenes Laertius book Lives of eminent philosophers written in the second century AD [6]:-这些主张的依据是什么呢？约公元450年左右写作的普罗克鲁斯（Proclus）是这些主张的依据，对于前四个定理，他在第三和第四种情况下引用了尤德默斯（Eudemus）的《几何学的历史》。尤德默斯是亚里士多德的学生。尽管尤德默斯的《几何学的历史》现已失传，但没有理由怀疑普罗克鲁斯。第五个定理被认为是泰勒斯的贡献，因为公元2世纪狄奥根尼斯·莱尔提乌斯（Diogenes Laertius）在他的著作《卓越哲学家的生平》中提到了一段相关的内容。Pamphile says that Thales, who learnt geometry from the Egyptians, was the first to describe on a circle a triangle which shall be right-angled, and that he sacrificed an ox (on the strength of the discovery). Others, however, including Apollodorus the calculator, say that it was Pythagoras.Pamphile声称，从埃及人那里学到几何学的泰勒斯是第一个在圆上描述一个直角三角形的人，并因此发现而献祭了一头牛。然而，其他人，包括计算家阿波洛多罗斯，说这是毕达哥拉斯的贡献。
