In this use the infinitive is said to depend on the word which it modifies ([p. 136]).
41. A kind of clause, consisting of a substantive in the objective case followed by an infinitive, may be used as the object of certain verbs.
Such clauses are called infinitive clauses, and the substantive is said to be the subject of the infinitive.
The subject of an infinitive is in the objective case.
Infinitive clauses are used (1) after verbs of wishing, commanding, advising, and the like, and (2) after some verbs of believing, declaring, and perceiving ([p. 138]).
An infinitive clause may be the object of the preposition for.
An infinitive clause with for may be used as a subject, as a predicate nominative, or as the object of a preposition ([pp. 138–139]).
42. The participle is a verb-form which has no subject, but which partakes of the nature of an adjective and expresses action or state in such a way as to describe or limit a substantive (pp. 12, 140).
43. A participle is said to belong to the substantive which it describes or limits (pp. 12, 142).
44. A participle should not be used without some substantive to which it may belong ([p. 142]).