| 1. | Order, proportion, and fitness pervade the universe .
秩序、均衡和公理遍及宇宙。 |
| 2. | The concern about this axiom stemmed from the fact .
对于这个公理的考虑是基于这样的事实。 |
| 3. | Enclid next lays down five postulates and five common notions .
接着Enclid就列出五个公设和五个公理。 |
| 4. | It seemed clear to him that this axiom could be dispensed with .
看来他清楚地认识到这个公理能够去掉。 |
| 5. | The simplest of the substitute axioms was suggested by him in 1969 .
最简单的代替公理是在1969年由他提出的。 |
| 6. | 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。 |
| 7. | The theorems should be deduced from axioms by purely logical arguments .
定理应该通过纯粹的逻辑的推导而从公理演绎得到。 |
| 8. | His axiom presupposes that there is an arbitrarily large radius at our disposal .
他的公理就是先假定有如我们意愿的任意大半径。 |
| 9. | Were this to happen, then the assumption of their parallel axiom would be invalid .
如果这一情况发生，他们的平行公理假设便会不正确。 |
| 10. | The fifth-century commentator proclus was very explicit about his objection to the parallel axiom .
第五世纪评论家Proclus非常明显地反对平行公理。 |
