on the point of

I was on the point of posting the letter when I saw it didn’t have a stamp on it.

我正准备寄信，突然发现上面没贴邮票。

The offices of aedile and tribune had disappeared, and by the end of the fourth century the quaestorship was on the point of disappearing.

传令官和保民官的头衔消失了，到四世纪末务官头衔也近于消失。