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The phrase "similar principles" is correct and usable in written English.
You can use it to describe principles that are similar to one another, as in the following example sentence: The two countries adopted similar principles in their economic policies.
Exact(57)
Similar principles apply in politics.
All of them function on similar principles.
Similar principles hold in civil-law countries.
His firm works on similar principles.
Wikipedia operates by similar principles.
Similar principles could apply to energy.
The MIT exoskeleton works using similar principles.
He produced a donkey choir on similar principles.
Similar(3)
The Epsom Range (1966) worked on similar principles, but used pre-formed plywood strips to create curved seats.
Similar principles may be applied to larger systems.
From streams to sets to fractals, there are similar principles at work.
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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