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譯者按:譬如有左中右三間房子靠在一起,要能认識清楚当中一间房子的特点,最好到左右两間里都看看,比較比較;我們在中学里接触的都是欧几里得几何的內容,但要认清其特点,最好也到非欧几何学的领域里“溜一趟”,关于罗巴切夫斯基的非欧几何,国內已有較多的介紹,而关于黎曼式非欧几何則介紹較少。現在特将苏联“数学教学”1961年第2期A.C.巴尔霍民柯的这篇文章編譯出来,供讀者从中窺視黎曼式非欧几何的大体輪廓。引言在几何学里經常有两件要做的主要工作,一是为了明确概念而确立定义,一是为了揭示真理而推証定理。每定义一新概念,必須有旧概念为依据,而此旧概念又須用更原始的概念去定义。如此追溯上去,我們不得不事先选定一組基本概念,不加定义,作为解释其余一切概念的出发点。
Translator’s note: If there are three houses on the left, right, and right, it is necessary to be able to understand the characteristics of one of the houses. It is better to have a look in both the right and left rooms and compare them; we are all in touch in Europe. The geometric content of a few miles, but to recognize its characteristics, it is best to “skid a trip” in the field of non-European geometry, on the Robachevski non-European geometry, there are more domestic Introduction, but less about Riemannian non-Euclidean geometry. Now compile this article of the “Mathematics Teaching” of the Soviet Union, A.C. Barkhin Minke, 2nd Issue, 1961, for readers to look at the general outline of Riemannian non-Euclidean geometry. INTRODUCTION In geometry, there are often two main tasks to be done. One is to establish the definition in order to clarify the concept, and the other is to deduce the theorem in order to reveal the truth. Every definition of a new concept must be based on the old concept, which must be defined by more primitive concepts. In retrospect, we have to select a set of basic concepts in advance and define them as the starting point for interpreting everything else.