(1) You have asked an excellent question. I have checked my books and
am happy to share what I learned.
(2) "I was happy to see him TO TAKE the lead."
(a) I believe that most books say that this is "bad" English.
(i) After verbs such as "see," you should not use "to." That is what
native speakers have decided.
(3) "I was delighted to see him TAKE the lead." (infinitive without "to")
(4) "I was delighted to see him TAKING the lead." (participle)
(5) Sentences #3 and #4 are "good" English.
(6) Do they mean the same?
(a) I am not sure.
(b) Some people may say that they mean the same.
(c) Some people may say they are a little different:
(i) Maybe (only maybe) "I was happy to see him TAKE the lead"=
You are referring to the whole situation. In other words, you are happy
that he is now No. 1.
(ii) Maybe (only maybe) "I was happy to see him TAKING the lead" =
You are emphasizing the action in progress.
(d) Here is another example that some people think is helpful:
(i) I saw him CROSS the street. = I saw him. He crossed the street.
(ii) I saw him CROSSING the street. = I saw him in the street. But I do not
know whether he finished, because I turned my head to do
something. Maybe he did not cross the street. Maybe he changed his
mind. Maybe he was hit by a car. I only saw him CROSSING the street --
only the action in progress.
***** Thank you *****
Student or Learner