1:1 Theophilus. The “former treatise” is clearly the gospel of Luke, both books being addressed to “Theophilus” (a name meaning “lover of God”). If Theophilus is not a generic name for anyone who is a lover of God, then the reference is evidently to a Roman official (as indicated by the adjective “most excellent” in Luke 1:3) in whom Luke had special interest, either seeking to lead him to Christ or to build him up in his newfound Christian faith.
1:1 Jesus began. Luke’s gospel contains the record of what Jesus began to do and teach. The implication is that Luke’s supplementary treatise tells what He continued to do and teach through the apostles by the enabling power of His Spirit, whom He sent to indwell and guide them at Pentecost.
1:3 infallible proofs. “Infallible proofs” is one word in the Greek (tekmerion) and occurs only this one time in the New Testament. It emphasizes that the evidences for Christ’s resurrection were not philosophical speculations but certain facts! It is appropriate that the word occurs only once, for no other event of Biblical history has been confirmed more certainly than His bodily resurrection. Not only His ten or more appearances to the disciples, but also the otherwise inexplicable evidence of the empty tomb, the remarkable change in the disciples, the development and spread of the church as a result of its preaching, the change to worship on the first day of the week, the age-long observance of Easter and the Lord’s supper, all in addition to the testimonies of the writers of the New Testament, as led and empowered by the Holy Spirit. These all combine to make it certain that Christ died for our sins and rose again for our justification.
1:3 forty days. As Jesus was victorious over His forty-day temptation by Satan (Luke 4:2), so He witnessed to His disciples for forty days of His greater victory over Satan through His death and resurrection (Hebrews 2:14-15).
1:5 baptized with the Holy Ghost. As John had “immersed” (literal meaning of baptizo) the disciples in water, they were shortly to be immersed in the Holy Spirit, in accordance with John’s prophecy (Mark 1:8) and Christ’s promise (John 14:16-17). He would henceforth immerse all future believers into the spiritual body of Christ (I Corinthians 12:13), to indwell them, guide them and be with them always.

