A participle will not be the main 
            verb in a sentence. Instead, as noted above, participles are verbs 
            that are used as modifiers. In Greek as in English, they may modify nouns as do adjectives, 
            or they may modify verbs, as do adverbs. To the extent that the 
            tense of a participle indicates time, it will indicate time only 
            relative to the main verb. Present tense participles usually 
            indicate action coincident with the 
            time of the main verb. In the sentence,
            He
                broke his leg playing football,
            the 
            main verb (also known as the "leading verb") is broke, and is 
            past tense. If this sentence were in Greek, the participle would be 
            in the present tense, but it would not indicate that the playing is 
            present time in an absolute sense. Rather it would indicate that the
            playing was present time at the moment the leg was broken. We 
            might translate, 
            He
                broke his leg while playing football.
            The presentation of
            the function of participles in your text book
            acknowledges the tendency of participle usage to refuse
            rigid classification. Nonetheless, I think it helpful
            to the beginner to have an outline of distinct
            classifications to use as an initial framework for
            interpreting participles. With the understanding that
            the following approach is intentionally simplistic,
            consider two ways in which participles are used, adjectivally and 
            adverbially.
            Participles used as Adjectives
            When a participle is
            in the attributive position, translate it as an
            adjective modifying the noun with which it agrees in
            gender, case and number. Remember that the fundamental 
            characteristic of the attributive position is that the adjective 
            comes immediately after its definite article.
            (a) One of the two basic patterns we have 
            learned for the attributive position is...  
            
            
            Definite Article | Noun | Definite Article |
            
            Adjective
            
            Previously, we have seen nouns, or 
            noun phrases, in the attributive position and functioning 
            adjectivally. Now we will see participial phrases doing the same 
            thing. 
            
            
            Definite Article | Noun | Definite Article |
            
            Participial Phrase
            
            
            Generally, then, we can simply think 
            of this form of the attributive construction in the following 
            manner: 
            
            
            Definite Article | Noun | Definite Article |
            
            Modifier
            
            
            EXAMPLE 1
            In the following sentence, we see the 
            familiar 
            ὁ 
            [noun]
            ὁ  
            [modifier] construction 
            wherein the modifier is in the attributive position.
            ὧδε
            ὁ
            νοῦς ὁ ἔχων σοφίαν
            Note that the modifier is the whole 
            phrase ἔχων σοφίαν, 
            "having wisdom."  It tells 
            us which νοῦς 
            (mind) is in view, the one having wisdom. The participle
            ἔχων 
            agrees with the noun it modifies, νοῦς, 
            in gender, case, and number. But the verbal idea in a participle is 
            not abandoned, and therefore it may take an object just as any other 
            verb may. In this sentence, although ἔχων 
            is functioning adjectivally, it is also a verb and has as its 
            object, σοφίαν.
            How do we translate this sentence?
            
            "Here [is] the mind, the having 
            wisdom [one]" is certainly awkward. 
            "Here [is] the having-wisdom 
            mind" is not any better.
            "Here [is] the mind having 
            wisdom" is perhaps marginally better. 
            
            But we can introduce an explanatory 
            object clause in English that will serve the same purpose as the 
            adjectival participle, viz., identifying what mind is in view:
            
            Here is the mind 
            that has 
            wisdom
            
            EXAMPLE 2
            ἐϐλασφήμησαν
            τὸ ὄνομα τοῦ θεοῦ τοῦ ἔχοντος τὴν ἐξουσίαν
            The leading verb is ἐϐλασφήμησαν, 
            the subject is implicit in the verb, and the object is ὄνομα. 
            The simple sentence is, "They blasphemed name." But ὄνομα 
            has some modifiers. Of course there is the definite article, and 
            that gives us, "They blasphemed the name." But then we have a 
            genitive τοῦ θεοῦ 
            that tells us what name, "the name of God." Now we come to the 
            participle, ἔχοντος. 
            It is masculine genitive singular and is very clearly in the 
            attributive position:
            τοῦ θεοῦ τοῦ
            ἔχοντος
            Clearly, it is modifying θεοῦ. 
            What God? "The God having..." But even though it is functioning as 
            an adjective, it is still a verb and can take an object. What does 
            God have? He has τὴν ἐξουσίαν. 
            The phrase τοῦ
            ἔχοντος τὴν ἐξουσίαν in its 
            entirety modifies θεοῦ, 
            telling us what God, even as the phrase τοῦ θεοῦ 
            itself modifies name, telling us what 
            name.
            How do we translate this sentence?
            
            "They blasphemed the name 
            of God, the having the power [one]" is certainly awkward. 
            "They blasphemed the name 
            of the-having-power God" is a little better.
            "They blasphemed the name 
            of God having power" doesn't get the job done.
            
            But we can introduce a relative clause in English that will serve the same purpose as the 
            adjectival participle, viz., identifying what god is in view, or 
            something about the God who is in view:
            
            "They blasphemed the name of 
            God who has the power."
            
            (b) Remember that the attributive 
            construction may also take the following form:
            
            Definite Article | 
            Adjective | Noun
            
            Again, in place of a simple 
            adjective, we may have a participial phrase. And we may represent 
            this form of the attributive construction generally as
            
            Definite Article | 
            Modifier | Noun
            
            EXAMPLE
            
            ἔλεγεν οὖν τοῖς 
            ἐκπορευομένοις ὄχλοις
 (Lk. 3:7)
            Therefore he was 
            saying to the going-out crowds...
            
            
            ἐκπορευομένοις modifes
            
            
            ὄχλοις, telling us 
            something about the crowds to whom Jesus was speaking. For this 
            reason, 
            
            ἐκπορευομένοις agrees with
            
            
            ὄχλοις in gender, case, 
            and number. We might well translate,
            Therefore he was 
            saying to the crowds that were going out...
            (c) Adjectives may function attributively 
            even though there is no definite article present. The same 
            is true for participial phrases.
            EXAMPLE
            καὶ ἐν τῇ συναγωγῇ ἦν ἄνθρωπος
            ἔχων πνεῦμα δαιμονίου ἀκαθάρτου
            Lk 
            4:33
            And in the synagogue was a man having a spirit of an unclean demon.
            The participial phrase
            ἔχων πνεῦμα δαιμονίου ἀκαθάρτου 
            (having a spirit of an unclean demon) describes the man who 
            was in the synagogue. For this reason, it agrees with ἄνθρωπος 
            in gender, case, and number. Again note that in English, a relative 
            clause might aptly be used to convey the idea of the participial 
            phrase:
            And there was a man 
            in the synagogue who had a spirit of an 
            unclean demon.
            (d) And finally, just as 
            is true of any adjective, a participle can function as a 
            substantive.
            EXAMPLE
            καὶ
            ἐγένετο φόϐος μέγας ἐπὶ
            πάντας τοὺς ἀκούοντας 
            Ac 5:5
            and great fear came upon all the hearing [ones]
            The noun modified by
            τοὺς ἀκούοντας 
            is not explicit, therefore we may need to supply a noun in English. 
            And again, we may translate using a relative clause to modify a 
            supplied pronoun:
            And great fear came 
            upon all those who heard.
            
            Participles used as
            Adverbs
        
        
            When a participle is
            not in the attributive position, it may well be
            functioning as an adverb, modifying the main verb by
            telling you when or in what manner the action of the
            main verb took place.
            EXAMPLE 1
            ὑπέστρεψαν
            εἰς Ἰερουσαλὴμ ἀναζητοῦντες αὐτόν
            ἀναζητοῦντες 
            [seeking] is functioning as an adverb, telling us in what manner
            ὑπέστρεψαν 
            [they returned].
            They returned unto Jerusalem 
            seeking him.
            But just as a participle used 
            adjectivally does not lose its verbal quality, neither does a 
            participle used adverbially lose its connection with a noun, whether 
            the noun is explicit or implicit. In this instance, the participle
            ἀναζητοῦντες 
            is masculine, nominative, plural. That is because it agrees with the 
            implied subject of the verb ὑπέστρεψαν. 
            Even when functioning as an adverb, the participle still has an 
            adjectival quality inasmuch as it agrees with and thus maintains 
            some modifying force on a substantive, whether explicit or implicit.
            EXAMPLE 2
            εὗρον αὐτον ἐν τῷ ἱερῷ
            καθεζόμενον ἐν μέσῳ τῶν
            διδασκάλων
            They found him in the 
            temple sitting in the midst of the teachers
            The subject of the sentence is "they," 
            implicit in the 3rd person, plural verb, εὗρον. 
            The object of the verb is αὐτον,
            "him". The participle καθεζόμενον
            [sitting] is adverbial telling us that someone was sitting 
            when "they found him in the temple." Who was sitting? Were they 
            sitting, or was he who was found sitting?
            While it may make practical or 
            contextual sense to you that the one who was found was doing the 
            sitting, there is a grammatical point that assures us of that fact.
            καθεζόμενον 
            agrees with αὐτον 
            in number (singular) case (accusative) and gender (masculine). It 
            would have to be nominative and plural to agree with the subject of εὗρον. 
            (In fact, εὗρον 
            itself could be either 1st person singular or 3rd person plural, but 
            the larger context from which this excerpt is taken, Luke 2:41ff, 
            indicates that the subject of the verb is Jesus' parents and 
            accordingly the verb is 3rd person plural.)
            When a participle is used 
            adverbially, we will often translate it using such temporal adverbs 
            as "while" or "after." As a rule of thumb, if the context calls for 
            a temporal adverb and if the participle is present tense, use 
            "while" or "when" rather than "after" in your translation. That is because a present tense participle usually indicates 
            action that is concurrent with the time of the leading verb. The 
            leading verb is the main verb, the verb of the simple sentence. In 
            the example above, the leading verb is εὗρον. 
            The present tense participle καθεζόμενον 
            is describing action that was concurrent with the time of the 
            leading verb. At the time that they found him, he was sitting in the 
            midst of the teachers. And we could translate this sentence as 
            follows: 
            They found him in 
            the temple while he was sitting in the midst of the teachers.
            Notice that  the present tense 
            participle καθεζόμενον 
            is translated using a past tense in English, was sitting. 
            As previously noted, the  tense of a participle does not 
            indicate absolute time of action, but very often does indicate relative time, that is, time relative to the 
            time of the leading verb. A present tense participle indicates 
            action occurring at the same time as the action of the main verb. In 
            this sentence, the present tense participle indicates action (sitting) 
            that was occurring at the time of the action of the main verb 
            (found). In English, we may use a past tense to indicate the same 
            idea.
            What if the sentence had been...
            
            εὗρον αὐτον ἐν τῷ 
            ἱερῷ καθεζομένῳ 
            ἐν μέσῳ τῶν διδασκάλων
            ...how would the meaning change? Now 
            the participle is in the dative case and no longer agrees with
            αὐτον. 
            Instead it agrees with 
            ἱερῷ. 
            Therefore it would be the temple that is described as sitting in the 
            midst of the teachers. Because the temple isn't likely to move, this 
            probably wouldn't mean "while it was sitting in the midst 
            of the teachers," and therefore we are apt to translate it 
            adjectivally rather than adverbially:
            They found him in 
            the temple which was sitting in the midst of the teachers.
            That illustrates two points: (1) You 
            must pay close attention to the case, number, and gender of the 
            participle in order to know who or what is the subject of the action 
            inherent in the participle, and (2) the particular function of the 
            participle, whether primarily adjectival or adverbial, may sometimes 
            only be discerned by considering the context and what makes the most 
            sense.
            EXAMPLE 3
            
            
            ἐλάλει εὐλογῶν τὸν θεόν. Lk. 
            1:64b
            
            He was speaking blessing God.
            The participle 
            
            εὐλογῶν functions as an adverb 
            modifying 
            
            ἐλάλει. It tells in what manner 
            "he was speaking." Even so, it still agrees with the implicit 
            subject of the verb in number, case, and gender.
            
            Reviewing what we have said, we 
            may conclude that an articular participle is necessarily attributive 
            and functions as an adjective (or substantive). In these cases, it 
            will often be helpful to use a relative clause in translation. If a participle is anarthrous, it may be attributive, or on the other hand, it may be 
            functioning adverbially. 
            It is true that anarthrous participle usage will 
            often defy neat categorization as either adjectival or adverbial. 
            But I think that as a beginning point, this framework will serve you 
            well. As you progress, you will get a feel for the wide range of 
            nuances conveyed by means of participles.