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The phrase "a further purpose" is correct and usable in written English.
It can be used when discussing an additional aim or objective in a context where multiple purposes are being considered.
Example: "In addition to improving efficiency, the new policy serves a further purpose of enhancing employee morale."
Alternatives: "an additional purpose" or "a supplementary aim".
Exact(19)
The inquiry is whether the work "adds something new, with a further purpose or different character, altering the first with new expression, meaning or message..
A further purpose of employing coring devices is to recover samples of the several layers of fine-grained deposits on the seafloor in such a way as to preserve the depositional sequence.
Because the stamp did not have a further purpose or different character, and because it had a commercial use, we conclude that this factor weighs strongly against fair use.
Put another way, the question is whether the new use, in the words of the Supreme Court, merely "supersedes the objects of the original creation, or instead adds something new, with a further purpose or different character".
A further purpose of the present work is to point out problems with finite horizon model predictive control applied to systems for which the optimal solution is a limit cycle.
In examining questions of fair use of copyrighted work, courts have looked at whether a new work transforms the original in a significant way, Ms. Jenkins said, citing a Supreme Court ruling that a legitimate work must add "something new, with a further purpose or different character, altering the first with new expression, meaning or message".
Similar(41)
The stamp does not reflect any "further purpose" than The Column.
For man is the only animal which causes pain to others without any further purpose than just to cause it.
Most of the wastes emitted from the food processing industries are not utilized for any further purpose.
It would be unreasonable simply to try to destroy an instance of a basic good, for no further purpose: for that would treat an instance of a basic good as something that it is not — that is, as valueless.
If every time a person is treated (or merely seen) by another, say, as an instrument (not a mere instrument) for some further purpose, we take it that the person in question is objectified, then it seems that in our daily lives we objectify nearly everyone, including ourselves.
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com