Declared (3724) (horizo from horos = boundary, limit; English "horizon" which is "the apparent line that divides the earth and the sky" which leads to the thought that Jesus is the "line" that divides all time into BC/AD!) means strictly speaking “to limit” and then figuratively “to fix,” “to appoint.” Time as well as space can be limited. Horizo means to mark out, to bound ("horizon") and figuratively to appoint, decree or specify. It means to mark out definitely. The boundary set can be (1) of time (fix, appoint - cf Heb 4:7) or (2) of space (fix, determine - Acts 17:26-27). Horizo referring to persons means to appoint or designate (Acts 17:31). In Lk 22:22 horizo refers to the making of a definite plan (decide, determine, cp Acts 2:23, 10:42, 11:29). BDAG adds that from the basic meaning., ‘to separate entities and so establish a boundary’, derives the sense ‘to define ideas or concepts’: set limits to, define, explain. In the Septuagint horizo can mean to act as a boundary (Nu 34:5), to separate or determine (Pr 18:18), to mark out (Pr 16:30), to establish, to ordain (3Macc 5:42) TDNT on horizo in Ro 1:4 - Jesus is instituted the Son of God in power. Whether the reference here is to a declaration or an appointment is not a matter of great urgency, since a divine declaration is also a divine appointment. In this present context horizo signifies that Jesus has been conclusively, irrefutably "marked out" as the "Son of God" by the resurrection. By Jesus' supreme demonstration of His ability to conquer death, a power belonging only to God, He established beyond "all reasonable doubt" (to use a term common in the legal vernacular) that He was indeed God, the Son. Horizo - 8 times in the NT - Usage: appointed(2), declared(1), determined(3), fixes(1), predetermined(1). Luke 22:22 "For indeed, the Son of Man is going as it has been determined; but woe to that man by whom He is betrayed!" Acts 2:23 this Man, delivered over by the predetermined plan and foreknowledge of God, you nailed to a cross by the hands of godless men and put Him to death. Acts 10:42 "And He ordered us to preach to the people, and solemnly to testify that this is the One who has been appointed by God as Judge of the living and the dead. Acts 11:29 And in the proportion that any of the disciples had means, each of them determined to send a contribution for the relief of the brethren living in Judea. Acts 17:26 and He made from one man every nation of mankind to live on all the face of the earth, having determined their appointed times and the boundaries of their habitation, Acts 17:31 because He has fixed a day in which He will judge the world in righteousness through a Man whom He has appointed, having furnished proof to all men by raising Him from the dead." Romans 1:4 who was declared the Son of God with power by the resurrection from the dead, according to the Spirit of holiness, Jesus Christ our Lord, Hebrews 4:7 He again fixes a certain day, "Today," saying through David after so long a time just as has been said before, "TODAY IF YOU HEAR HIS VOICE, DO NOT HARDEN YOUR HEARTS." Horizo - 20x in the non-apocryphal Septuagint - Nu 30:2, 3, 4, 11; Nu 34:6; Josh 13:7, 27; Josh 15:12; 18:20; 23:4; Pr 16:30; 18:18; Ezek 47:20; Dan 6:12; The story is told that a certain M. Lepeau complained to Talleyrand that a new religion of his—one he considered a great improvement over Christianity—had failed to catch on with the people. He asked Talleyrand for some suggestions. Talleyrand dryly said, M. Lepeau, to insure success for your new religion, all you need do is have yourself crucified and then rise from the dead on the third day! Son of God - Jamieson writes... Observe how studiously the language changes here. He “was made [says the apostle] of the seed of David, according to the flesh” (Ro 1:3); but He was not made, He was only “declared [or proved] to be the Son of God.” So Jn 1:1, 14, “In the beginning was the Word … and the Word was made flesh”; and Is 9:6, “Unto us a Child is born, unto us a Son is given.” Thus the Sonship of Christ is in no proper sense a born relationship to the Father, as some, otherwise sound divines, conceive of it. By His birth in the flesh, that Sonship, which was essential and uncreated, merely effloresced into palpable manifestation. (See on Lk 1:35; Acts 13:32,33). With power - Clearly the power capable of raising one from the dead. NET has this note - Paul is not saying that Jesus was appointed the "Son of God by the resurrection" but "Son-of-God-in-power by the resurrection," as indicated by the hyphenation. He was born in weakness in human flesh (with respect to the flesh, Ro 1:3) and he was raised with power.