Luke 2:1

1Now
Grk “Now it happened that.” The introductory phrase ἐγένετο (egeneto, “it happened that”), common in Luke (69 times) and Acts (54 times), is redundant in contemporary English and has not been translated.
in those days a decree
This decree was a formal decree from the Roman Senate.
went out from Caesar
Or “from the emperor” (“Caesar” is a title for the Roman emperor).
Augustus
Caesar Augustus refers to Octavian, who was Caesar from 27 b.c. to a.d. 14. He was known for his administrative prowess.
to register
Grk “that all the empire should be registered for taxes.” The passive infinitive ἀπογράφεσθαι (apografesqai) has been rendered as an active in the translation to improve the English style. The verb is regarded as a technical term for official registration in tax lists (BDAG 108 s.v. ἀπογράφω a).
This census (a decree…to register all the empire) is one of the more disputed historical remarks in Luke. Josephus (Ant. 18.1.1 [18.1–2]) only mentions a census in a.d. 6, too late for this setting. Such a census would have been a massive undertaking; it could have started under one ruler and emerged under another, to whose name it became attached. This is one possibility to explain the data. Another is that Quirinius, who became governor in Syria for the later census, may have been merely an administrator for this census. See also Luke 2:2.
all the empire
Grk “the whole (inhabited) world,” but this was a way to refer to the Roman empire (L&N 1.83).
for taxes.
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