Updated: Sep 24, 2020
8. The time of writing. To Beza and Gomarus he appears to have written before Matthew, the reasons for which are recalled to the anvil.
Concerning the time of the writing of Luke’s Gospel, there is no agreement.That it was written in the fifteenth year after the ascension of the Lord, Theophylact asserts.The Arabic Codex of Kirstenius persists in saying that it was written later, namely, in the fourteenth year of Claudius, the twenty-second year after the ascension of Christ into Heaven.Those that contend that not until the twenty-seventh year after the ascension was the Gospel written together with Acts are not wanting.It is not able to be determined by trustworthy reasons which one rightly defines the time.Most of the ancient Fathers assert that Matthew wrote his Gospel before Mark, and Mark before Luke.Nevertheless, the Most Learned Beza, Annotationibus majoribus on verse 1, and Gomarus, following Beza, on Luke 1, lean toward the contrary position by these arguments, that Luke himself in Luke 1:1 declares that those that had before him written the history of Christ undertook that writing rashly, in such a way that they had no πληροθορίαν, full assurance, of their writings, and he, fully following all things, considered it necessary to write the history of Christ ἀκριβῶς/accurately:that in verse 2 he says that he wrote καθὼς παρέδοσαν, as they delivered to us, which from the beginning were eyewitnesses and ministers of the matter; since this delivery by tradition is to be referred to preaching, not to preceding writing, thence it is gathered that others did indeed preach before Luke wrote, but none wrote:finally, that, if Matthew and Mark had written before Luke, Theophilus, to whom Luke wrote, would have had no need that of those things, that of those things in which he had been instructed concerning the doctrine of the Gospel, he should recognize theἀσφάλειαν/certainty, which certainly he had been able to draw from the Gospels of Matthew and Mark, if those had already existed.But those arguments do not appear so firm that on account of those that most ancient and harmonious, if Irenæus be excluded, authority of the ancients, who assert that Matthew wrote first, ought to be deserted.For, by the verb ἐπεχείρησαν, they have taken in hand or attempted (which term the most learned Philologists, Casaubon, Grotius, and others, establish to be neutral), Luke does not indicate an unsuccessful attempt on the part of those preceding, as if they had not perfected their designs, but rather he commends those that anticipated this sort of study, and associates himself with them.On that account in verse 3 he says:ἔδοξεκἀμοί, it seemed good to me also.As if he should say, that he appeared to himself to undertake the very thing that those preceding him had undertaken.Then, συντάξασθαιλόγον, to set a matter in order, is not to repair ἀτελέςτι, something imperfect.But those preceding are also said to have prepared a narration concerning matters πεπληροφορημένοις, most surely believed, in which they had full confidence, and so not uncertain or doubtful:in such a way that Luke both confirms that narration, and attributes πληροφορίας, full assurance, to those narrating the testimony.Also, that παράδοσις/tradition, of which mention in made in verse 2, is not so much of the λόγου/word preached, as of ἐπιστολῆς/Epistle and pen (2 Thessalonians 2:15), and is referred, not so much to τὰπεπληροφορημένα, the things most surely believed, as to the written διήγησιν/declaration/narration.Finally, it was the scope of Luke’s writing, that Theophilus might know the certainty of those reports/ words, wherein κατηχήθης, he had been instructed.Therefore, that very thing, which Theophilus had already been taught, namely, in preceding written διηγήσει/declaration/narration, he desired to write anew for the sake of Theophilus, and of all the faithful, and thus to beget greater ἀσφάλειαν/ certainty.Therefore, he wrote after Matthew and Mark.But in what year exactly he wrote, it is unclear.
 Claudius reigned as Roman Emperor from 41 to 54.  Luke 1:1: “Forasmuch as many have taken in hand to set forth in order a declaration of those things which are most surely believed (τῶν πεπληροφορημένων) among us…”  Luke 1:3: “It seemed good to me also, having had perfect understanding of all things from the very first, to write unto thee in order (παρηκολουθηκότι ἄνωθεν πᾶσιν ἀκριβῶς καθεξῆς σοι γράψαι), most excellent Theophilus…”  Luke 1:2: “Even as they delivered (παρέδοσαν) them unto us, which from the beginning were eyewitnesses, and ministers of the word…”  Luke 1:4: “That thou mightest know the certainty of those things, wherein thou hast been instructed (ἵνα ἐπιγνῷς περὶ ὧν κατηχήθης λόγων τὴν ἀσφάλειαν).”
Dr. Dilday's Lecture: "The Exaltation of Christ, Part 4"