Here is a response that I made some years ago to a question about Luke 10:18.
Okay [Mike], here we go.
As I mentioned last night, the information you requested is actually on page 67 of Goodwin's syntax and can be found in section 146 under aorist participles.
"The Aorist Participle used as an integral part of the object of a verb of perception represents the action which it denotes as a simple event without defining its time. The action may be one which is directly perceived and hence coincident in time with that of the principal verb, or it may be one which is ascertained or learned, and hence antecedent to the action of the principal verb. In the latter case it takes the place of a clause of indirect discourse having its verb in the Aorist Indicative.
Acts 9:12; KAI EIDEN ANDRA . . . ANANIAN ONOMATI EISELQONTA KAI ETIQENTA AUTWi XEIRAS, and he has seen a man named Ananias come in and lay hands upon him. See also Luke 10:18; Acts 10:3; 11:3; 26:13; 2 Pet. 1:18.
Luke 4:23; hOSA HKOUSAMEN GENOMENA, whatever things we have heard to have been done."
That is what Goodwin says verbatim.
Looking at the NWT rendering, "I began to behold Satan already fallen like lightning from heaven," it seems that the NWT construes EQEWROUN (1st singular imperfect indicative active) as having ingressive (inceptive) force. This strategy is fine in light of what K.L. McKay writes in A Syntax of the Verb in NT Greek (pages 29-30):
"The imperfective aspect presents an activity as going on, in process, without reference to its completion. This may consist of a single activity in process at the time of reference, or a series of repetitions of an action, whether consecutively by one agent or distributively by a number of agents, regarded as parts of a wider whole activity. According to its context an activity in process may imply a notion of attempting, continuing, setting about, beginning or the like, and a variety of English translations may be needed to represent one Greek form."
See Mt 5:2.
As for the "already fallen" rendering of PESONTA, it appears that the NWT simply construes the aorist participle as denoting antecedent action (i.e., Jesus began to see an event that had already occurred [began to occur] before he started to perceive it) by using the English past participle "fallen" coupled with the adverbial "already."
I must admit that after reading Stanley Porter's works and consulting Buist Fanning, my understanding of aorist participles has shifted somewhat. If you care to read Porter's dense monograph on aspect, see Verbal Aspect in the Greek of the NT, With Reference to Tense and Mood (New York: Peter Lang, 1989). Frankly I think he provides one of the most "scientific" accounts of aorist participles. Having said the foregoing, I believe the NWT rendering is not problematic from a translational standpoint.
As an update to this old post, I must point out that Porter has been thoroughly criticized by Chrys Caragounis. The latter scholar argues (somewhat convincingly) that Porter has misrepresented how Greeks understand tense and aspect.