I'm currently taking a first year Greek class, and we've finally gotten around to studying the use of participles in the Greek.
While it can truly be said that Greek uses prepostions with a "mathematical exactness and a scientific precision"... much more so even, than the use of prepositions in English... the same thing cannot be said about the Greek use of participles.
I dug out my old copy of "Fundamentals of Greek Research" by Walter J. Cummins. FoGR contains a few rudimentary items that are useful, such as how to use a concordance, the meanings of some of the most common prepositions, and a crude synopsis of Greek tenses, but for the most part FoGR uses examples of interpretation taken from PFAL, and reinforces those interpretations, even when the Greek does not necessarily do so. There was NO mention of participles. The closest is in a quote from page 21, "Other parts of speech and constructions are used just as precisely as the prepositions. The Greeks were a very mathematical people, and so was their language."
That's just not true. The Greek thinking behind participles was so different from our way of thinking about participles, a direct translation of a participial phase into English usually doesn't make sense. Translating a participial phrase from Greek into English REQUIRES guesswork, informed by information from other parts of the sentence.
Most of the big debates, about what particular passages from the New Testament mean, involve a participial phrase. The example our professor brought up spontaneously in class was Acts 19:2a, "He said unto them, Have ye received the Holy Ghost since ye believed?" The phrase "since ye believed" is the translation of a single Greek participle, and could just a accurately be translated "when ye believed" or "because ye believed."
Wierwille taught us that interpretation of the Bible has a degree of certainty which in truth, it does not have. Of course Wierwille's goal was for us to accept HIS interpretation as the only one having mathematical exactness and scientific presion. It had neither.
Love,
Steve