All 7 Uses of

consequence
in
Utopia, by Thomas More

Upon these reasons it is, that I think putting thieves to death is not lawful; and it is plain and obvious that it is absurd and of ill consequence to the commonwealth that a thief and a murderer should be equally punished; for if a robber sees that his danger is the same if he is convicted of theft as if he were guilty of murder, this will naturally incite him to kill the person whom otherwise he would only have robbed; since, if the punishment is the same, there is more security, and less danger of discovery, when he that can best make it is put out of the way; so that terrifying thieves too much provokes them to cruelty.†

consequence = result

…that the trouble of keeping it was equal to that by which it was gained; that the conquered people were always either in rebellion or exposed to foreign invasions, while they were obliged to be incessantly at war, either for or against them, and consequently could never disband their army; that in the meantime they were oppressed with taxes, their money went out of the kingdom, their blood was spilt for the glory of their king without procuring the least advantage to the people, who…

consequently = resultantly (as a result)

When they have thus taken care of their whole country, and laid up stores for two years (which they do to prevent the ill consequences of an unfavourable season), they order an exportation of the overplus, both of corn, honey, wool, flax, wood, wax, tallow, leather, and cattle, which they send out, commonly in great quantities, to other nations.†
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consequences = results

As they came to treat of affairs of great consequence, the deputies from several towns met together to wait for their coming.†
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consequence = importance

If any man imagines that there is a real happiness in these enjoyments, he must then confess that he would be the happiest of all men if he were to lead his life in perpetual hunger, thirst, and itching, and, by consequence, in perpetual eating, drinking, and scratching himself; which any one may easily see would be not only a base, but a miserable, state of a life.†

consequence = result

and if such a thing should fall out, for man is a changeable creature, yet, there being few priests, and these having no authority but what rises out of the respect that is paid them, nothing of great consequence to the public can proceed from the indemnity that the priests enjoy.†

consequence = importance

, the unconquered King of England, a prince adorned with all the virtues that become a great monarch, having some differences of no small consequence with Charles the most serene Prince of Castile, sent me into Flanders, as his ambassador, for treating and composing matters between them.†

Definitions:

(1) (consequence as in: a direct consequence of)
a result of something (often an undesired side effect)
(2) (consequence as in: of little consequence)
importance or relevance
(3) (meaning too rare to warrant focus)
meaning too rare to warrant focus:

In classic literature, consequential may refer to someone with too much feeling of self-importance as when Dickens wrote "Because he's a proud, haughty, consequential, turned-up-nosed peacock."

Self-consequence was used in a similar manner, but is more easily understood by modern readers since important is one of the modern senses of consequence.

Another classic sense of consequent that is similar to importance or significance refers to "material wealth or prominence" as when Jane Austen wrote: "They had each had money, but their marriages had made a material difference in their degree of consequence."