| The unique parallel of Euclid is just a sophism in order to trap ignorant people. |
| Speculative geometry contains elementary geometry which is not all based on Euclid. |
| His commentary to Euclid is of interest because of its discussion of unordered irrationals. |
| The work of both Aristaeus and Euclid on conics was, almost 200 years later, further developed by Apollonius. |
| So when Euclid described his geometry, many believed it to be the one true geometry. |
| Euclid made repeated use of axioms that he had not stated, without which his arguments are not logically valid. |
