Matthew 3:17

Could it be benefical to read Greek dictionaries on this word to find my answer?

Consider the possibility that the answer is better considered by syntax and semantics than by vocabulary and grammar.

I do not understand what you mean MJ. Can you explain? I always have believed syntax refers to grammar, while semantics refers to meaning. I have read commentaries but I do not see anything on the Greek form of Matthew 3:17. 

Syntax is a narrower field than grammar -- syntax emphasizes context which contributes more to the understanding of the meaning. My experience is that grammar books are used from the beginning in classes for dead languages; syntax books are introduced in the 2nd or 3rd year.

In linguistics, the grammar of a natural language is its set of structural rules on speakers' or writers' usage and creation of clauses, phrases, and words. The term can also refer to the study of such rules, a subject that includes phonology, morphology, and syntax, together with phonetics, semantics, and pragmatics. There are, broadly speaking, two different ways to study grammar: traditional grammar and theoretical grammar. . . . 

Outside linguistics, the word grammar often has a different meaning. It may be used more widely to include rules of spelling and punctuation, which linguists would not typically consider as part of grammar but rather of orthography, the conventions used for writing a language. It may also be used more narrowly to refer to a set of prescriptive norms only, excluding the aspects of a language's grammar which do not change or are clearly acceptable (or not) without the need for discussions. Jeremy Butterfield claimed that, for non-linguists, "Grammar is often a generic way of referring to any aspect of English that people object to".

For syntax, I'd fault the Wikipedia for including constituency structures but not dependency. But note it's intermediary role between form (pure grammar) and semantics.

In linguistics, syntax (/ˈsɪntæks/ SIN-taks) is the study of how words and morphemes combine to form larger units such as phrases and sentences. Central concerns of syntax include word order, grammatical relations, hierarchical sentence structure (constituency), agreement, the nature of crosslinguistic variation, and the relationship between form and meaning (semantics). There are numerous approaches to syntax that differ in their central assumptions and goals.

Semantics (from Ancient Greek σημαντικός (sēmantikós) 'significant') is the study of reference, meaning, or truth. The term can be used to refer to subfields of several distinct disciplines, including philosophy, linguistics and computer science. 

My point was that grammatical form of a word is a small sliver of the meaning - look at the tools that will provide the most useful information. Or, put another way, how much time in your high school study of Canterbury Tales or Beowulf or even Shakespeare did you spend discussing the case form of the word?

Why is this translation of εὐδόκησα not in the past tense?

The only reliable to this question is "because the translator(s) thought their translation more accurately caught the meaning of the text than a past tense" ... unless the translator(s) provide a note explaining their choice this is the only answer that you know to be correct. The morphological form is only one element that determines the author's intending meaning and to over emphasize it is to misunderstand the text.

Is this question un-answerable due to the Greek language?

It is true of any translation.

To answer your question - which use of these uses of the aorist do you think is being used:

[quote]

Determining the use of a tense is necessarily an exegetical decision involving a degree of subjectivity. But by carefully considering the following factors, you will have a more objective basis for determining the use of a tense:

1. Lexical meaning (the verb stem specifies an action that is punctiliar, progressive, stative, etc.)
2. Grammar (e.g., the voice, mood, transitiveness of the verb)
3. Context (additional information about the nature of the verb’s action)

In each section of tense usage, the use listed first occurs most frequently. The rest of the uses are special uses of the tense in the sense that they occur less frequently.

Aorist

The aorist may be translated as a simple past, as a present, as a perfect, and occasionally as a future. The lexical meaning of the verb, the context, and other grammatical features determine the use of the aorist. Only in the indicative does the the aorist have a time element. In the other moods, its timeless and indefinite nature is more apparent.

Constative Aorist

Function

The constative aorist presents the action of the verb as a simple whole without regard to the parts of the action or the time involved. The constative aorist best exemplifies the basic meaning of the aorist.

Examples

τεσσεράκοντα καὶ ἕξ ἔτεσιν οἰκοδομήθη ὁ ναὸς οὗτος. (John 2:20)
This temple was built in forty-six years.

καὶ ἐβασίλευσαν μετὰ τοῦ Χριστοῦ χίλια ἔτη. (Rev. 20:4)
And they reigned with Christ for a thousand years.

For more examples, see Matt. 22:28; Rom. 14:3.

Ingressive Aorist

Function

The ingressive aorist stresses the beginning of an action or the entrance into a state or condition. The lexical meaning of the verb stem is usually involved in conveying this sense. The ingressive aorist normally occurs with two types of verbs: (1) with stative verbs, emphasizing the entrance into the state, and (2) with verbs denoting new activity.

Examples

διʼ ὑμᾶς ἐπτώχευσεν. (2 Cor. 8:9)
For your sake He became poor.

καὶ εἶδον … τὰς ψυχὰς τῶν πεπελεκισμένων … καὶ ἔζησαν. (Rev. 20:4)
And I saw … the souls of those who had been beheaded … and they came to life.

For more examples, see Matt. 9:27; Mark 10:21; Luke 15:32; Acts 15:13.

Culminative Aorist

Function

The culminative aorist stresses some action from the viewpoint of the conclusion or result of the act. It may often be translated by an English perfect. Some verbs are inherently culminative in their meaning (e.g., to die, to arrive, to be persuaded).

Examples

ἐγὼ γὰρ ἔμαθον … αὐτάρκης εἶναι. (Phil. 4:11)
For I have learned … to be content.

ἤγαγεν αὐτὸν πρὸς τὸν Ἰησοῦν. (John 1:42)
He brought him to Jesus.

For more examples, see Matt. 27:20; Acts 5:4; Acts 13:43; Rev. 5:5.

Gnomic Aorist

Function

The gnomic aorist expresses some generally accepted fact or truth. The aorist is appropriate because time does not affect these truths. Such truths are often stated in a proverbial fashion. Generally, a gnomic aorist can be translated by the English present.

Examples

ἐξηράνθη ὁ χόρτος καὶ τὸ ἄνθος ἐξέπεσεν. (1 Pet. 1:24)
The grass dries up, and the flower falls off.

καὶ ἐδικαιώθη ἠ σοφία ἀπὸ πάντων τῶν τέκνων αὐτῆς. (Luke 7:35)
And wisdom is justified by all its children.

For more examples, see Matt. 23:2; James 1:24.

Clarification

Occasionally the aorist is used after a condition (either real or implied) almost as a future. These instances should be considered gnomic aorists (cf. Gal. 5:4).

ἐὰν μή τις μένῃ ἐν ἐμοί, ἐβλήθη ἔξω. (John 15:6)
If anyone remains not in Me, he will be cast out.

Epistolary Aorist

Function

In using the epistolary aorist, a writer adopts the time frame of his audience and, writing from their time perspective, describes something as already past that is presently happening or has not happened yet. The epistolary aorist should be translated in the present.

Examples

ὅν ἔπεμψα πρὸς ὑμᾶς (Col. 4:8)
whom I send to you

ὃν ἀνέπεμψα σοι (Philem. 12)
whom I send to you

For more examples, see Phil. 2:28; Gal. 6:11.

Futuristic Aorist

Function

The futuristic aorist describes a future event as though it were already complete to emphasize the certainty of the event.

Examples

πάντα ὅσα προσεύχεσθε καὶ αἰτεῖσθε, πιστεύετε ὅτι ἐλάβετε, καί ἔσται ὑμῖν. (Mark 11:24)
All things for which you are praying and asking, believe that you will receive [them], and you will have them [lit. they will be to you].

ἐν τούτῳ ἐδοξάσθη ὁ πατήρ μου, ἵνα καρπὸν πολὺν φέρητε. (John 15:8)
My Father will be glorified in this, that you bear much fruit.

For more examples, see Matt. 18:15; Heb. 4:10.

Dramatic Aorist

Function

The dramatic aorist sometimes mentions a present event as if it were a past event in order to dramatize the action or make it vivid. Translate the dramatic aorist using the English present.

Examples

ἔγνων τί ποιήσω. (Luke 16:4)
I know what I will do.

For more examples, see Mark 1:11; John 11:41.

Bob Jones University Greek Faculty, A Handbook for New Testament Greek: Forms and Syntax, ed. Lincoln Mullen, Fourth Edition (Greenville, SC: Bob Jones University Press, 2007), 231–235.

In this case I also found it useful to decide if the verb is stative or active.

Then there is the question of the use of the verb:

[quote]

εὐδοκεῖν. A late word (see Sturz. de dial. Mac. 168) not found in the Attic writers, constructed (1) with the infinitive in the sense of ‘to be pleased,’ i.e. ‘to resolve,’ εὐδοκοῦμεν μᾶλλον ἐκδημῆσαι, 2 Cor. 5:8; (2) with accusative (see ch. 12:18), ‘to be pleased with,’ ‘take delight in:’ ὁλοκαυτώματα οὐκ εὐδόκησας, Hebr. 10:8; εὐδόκησας, κύριε, τὴν γῆν σου, Ps. 84:1; (3) with εἰς and ἐν with the same meaning as (2) or ‘to be pleased in,’ i.e. to place one’s purpose, decision, or resolution in a thing or person. Here the sense is: My Son, the Beloved in whom my pleasure rests, in whom my plan for the salvation of mankind is centred. Cp. Eph. 1:9, γνωρίσας ἡμῖν τὸ μυστήριον τοῦ θελήματος αὐτοῦ κατὰ τὴν εὐδοκίαν αὐτοῦ ἣν προέθετο ἐν αὐτῷ. εὐδοκεῖν answers to εὐδοκίαν προθέσθαι.

A. Carr, The Gospel according to St Matthew, Cambridge Greek Testament for Schools and Colleges (Cambridge: Cambridge University Press, 1896), 103.

Then there are the notes provided (in my mind) primarily for translators:

[quote]

b. aorist act. indic. of εὐδοκέω (LN 25.87) (BAGD 2.a. p. 319): ‘to be well pleased (with/in)’ [BAGD, BNTC, CC, NTC, PNTC, WBC; CEV, ESV, GW, KJV, NASB, NIV, NRSV], ‘to be very pleased (with)’ [BECNT; NCV], ‘to be pleased (with)’ [LN; TEV], ‘to be delighted (with)’ [NICNT], ‘to take delight (in)’ [BAGD; REB], ‘to take great delight (in)’ [NET], ‘to come to delight (in)’ [NIGTC], ‘to take pleasure (in)’ [LN]. The phrase ‘in whom I am well-pleased’ is translated ‘who brings me great joy’ [NLT]. This verb means to be pleased with something or someone, with the implication of resulting pleasure [LN]. . . .

QUESTION—Why was the Father ‘well pleased’ with the Son?
God was pleased with Jesus as the Messiah and Suffering Servant [PNTC]. It suggests his pre-temporal election as Messiah [EBC, Lns]. The Father was pleased by Jesus being baptized [BECNT, BNTC, NICNT]. The Father was pleased that Jesus has accepted the role of Suffering Servant [ICC]. The Father has been delighted in the Son from all eternity, but is also pleased with the Son’s acceptance of his mission of atoning for sin [NTC]. The aorist verb is used in a way similar to a perfect tense, and means that God’s pleasure continues to remain on Jesus [CC]. It is a timeless aorist [NTC].

David Abernathy, An Exegetical Summary of Matthew 1–16, Exegetical Summaries (Dallas, TX: SIL International, 2013), 72-73.

From these, you should be able to put together a full answer.