中文摘要：

熟知欧氏参数曲面在非脐点处有且仅有两个相互垂直的主方向。对相互垂直的理解是容易的，但文献[3]的处理方法在实际教学中，学生理解主方向只有两个时存在模糊之处。本文目的是仔细分析这些模糊之处及产生的原因，并给出较为清晰的补充修缮，以更好地为教学服务。

英文摘要：

It is known that there are exactly two perpendicular principal directions at a non umbilical point on a parameterized surface. It is easy to understand that the two principal directions are perpendicular. However, omissions and ambiguities still exist in[3] concerning to explain why there are exactly two principal directions. This paper tries to analyze the reasons and clean omissions and ambiguities, aiming to serve the teaching well.