Analysis.
The +infinitive phrase+ may be used +after a preposition+ as the +principal term+ of another phrase.
1. My friend is about to leave me.
\to
\ leave | me
\———-'——
\ about |
\ / \
\————————-
|
friend | is \ / \
========|=====================
\My |
+Explanation+.—The preposition about introduces the phrase used as attribute complement; the principal part is the infinitive phrase to leave me.
2. Paul was now about to open his mouth. 3. No way remains but to go on.
+Explanation+.—But is here a preposition.
The +infinitive+ and its +assumed subject+ may form the +principal term+ in a phrase introduced by the preposition +for+.
4. For us to know our faults is profitable.
us
———-
| \to
\ | \ know | faults
\For | \———'————
\ / \ \our
\———-
|
/ \ | is \ profitable
=============|======================
|