Both Uses

resolve
in
Resistance to Civil Government
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As they could not reach me, they had resolved to punish my body;
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resolved = decided
Paley, a common authority with many on moral questions, in his chapter on the "Duty of Submission to Civil Government," resolves all civil obligation into expediency; and he proceeds to say that "so long as the interest of the whole society requires it, that is, so long as the established government cannot be resisted or changed without public inconvenience, it is the will of God ...that the established government be obeyed—and no longer.†

Definitions:

(1) (resolve as in: I resolved to stop drinking.)
to decide -- typically a firm or formal decision

In modern writing resolve is typically used to emphasize a firm or formal decision. In classic literature, it is used more frequently and often simply replaces decide or determine.
(2) (resolve as in: This committee hereby resolves...)
make a decision or voice an opinion by formal group vote
(3) (resolve as in: Her resolve weakened.)
firmness of purpose (strong determination to do something)
(4) (resolve as in: How was the problem resolved?)
to solve a problem, settle a disagreement, or for a situation to change
(5) (meaning too rare to warrant focus)
Less commonly, resolve can mean:
- to make clearly visible -- as in "The microscope cannot resolve that level of detail."
- to divide into parts -- as in "The problem resolves into three parts,"or (math) "Resolve the polynomial into factors," or (chemistry) "As the temperature changes, the compound resolves into its component parts," or (physics) "The force on the inclined plane resolves into horizontal and vertical components."
- reduce or convert into something else -- as in "The URL is resolved to an IP address," or (music) "The progression is resolved as the dissonance is replaced by consonance."