Again, as user Edwin Ashworth said in a comment, it is best paraphrased by 'for this reason'.
The importance of Amphipolis in ancient times was due to the fact that it commanded the bridge over the Strymon, and consequently the route from northern Greece to the Hellespont; it was important also as a depot for the gold and silver mines of the district, and for timber, which was largely used in shipbuilding.
It is characteristic of early literature that the evolution of the thought - that is, the grammatical form of the sentence - is guided by the structure of the verse; and the correspondence which consequently obtains between the rhythm and the grammar - the thought being given out in lengths, as it were, and these again divided by tolerably uniform pauses - produces a swift flowing movement, such as is rarely found when the periods have been constructed without direct reference to the metre.
You can complete the definition of consequently their given by the English Definition dictionary with other English dictionaries: Wikipedia, Lexilogos, Oxford, Cambridge, Chambers Harrap, Wordreference, Collins Lexibase dictionaries, Merriam Webster.
Consequently, staff members become better motivated, and productivity increases.
As those states finally yielded, the Union was strengthened by reason of a greater equality and consequently less jealousy among the original states, and the United States came into possession of the first territory in which all the states had a common interest and out of which new states were to be created.