| 1. | Some of these are mistakes made by euclid that can be remedied .
有些错误是欧几里德搞错的，可以纠正。 |
| 2. | Where euclid unconsciously assumed the infinitude of straight lines .
欧几里德不自觉地假定了直线的无限性。 |
| 3. | He did not grant independent existence to the non-euclidean geometries .
他不承认非欧几里德几何的独立存在性。 |
| 4. | The axioms adopted by euelid mere supposed to be self-evident truths .
欧几里德用的公理都应看作是不证自明的真理。 |
| 5. | The common conclusion was the uniqueness and necessity of euclidean geometry .
欧几里德几何的唯一性与必要性已被公认。 |
| 6. | The non-euclidena geometries were in effect subordinated to euclidean geometry .
非欧几里德几何实际上是从属于欧几里德几何的。 |
| 7. | Science should always try to use euclidean geometry and vary the laws of physics where necessary .
科学应该永远试用欧几里德几何学，并在必要处改变物理定律。 |
| 8. | Each innovation destined to dwarf the one extensive accomplishment of the greeks-euclidean geometry .
每一个创新都注定希腊人的巨大成就--欧几里德几何相形见绌。 |
| 9. | The advent of the theory of relativity forced a drastic change in the attitude toward non-euclidean geometry .
相对论的发现迫使对待非欧几里德几何的态度有激烈的变化。 |
