Dictionary
parallelly
adverb
In a parallel direction; in a parallel manner.
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The word "parallelly" is not correct in written English.
The correct word is "parallely". If you are referring to two or more things that are occurring at the same time, you can use the word "parallely" in a sentence like this: The two students worked parallely on their essays, finishing them at the same time.
Exact(1)
This natural motion occurs on the basis of an effective infinitesimal tendency of persistence, that parallelly displaces the spacetime direction \(R\) of a body at an arbitrary point \(p\) on its trajectory to a neighbouring point \(p'\) that lies in the direction \(R\) at \(p\).
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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