on the point of (doing something)
Ready or about to do something. I'm sorry I'm running late—I was on the point of getting in the shower when the doorbell rang. We have several products on the point of becoming global successes. We just need another strong marketing push.
on the point of
Also, at the point of. On the verge of, close to, as in I was on the point of leaving when the phone rang. The first term dates from the late 1200s, the second from the first half of the 1500s.