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The phrase "on the same principles" is correct and usable in written English.
It can be used when discussing similarities in reasoning, methods, or beliefs between different subjects or situations.
Example: "The new policy was implemented on the same principles as the previous one, ensuring consistency in our approach."
Alternatives: "based on the same principles" or "following the same principles."
Exact(58)
Basically all betting markets operate on the same principles: make sure no one knows more than you do".
On the same principles, white men were made slaves.
Manage wall-trained loganberries and tayberries on the same principles.
Bras are an incredibly complex design and work on the same principles as the cantilevered bridge.
The resultant organization was stable but open to change on the same principles.
Heat pumps are based on the same principles as a household refrigerator.
Both operate on the same principles, but each has its own attractions for the ship designer.
This could be pretty cool.'" The Beatles: Rock Band works on the same principles as other interactive music games.
"Building a business, being a champion, being physically fit all is based on the same principles," she said.
Nationwide offers an account which runs on the same principles as High 5, albeit with less attractive rates.
That growth has been based on the same principles at all levels of the club - principles of style and substance.
More suggestions(14)
on the same conditions
on the same tenets
on the same precepts
on the same policy
on the same declaration
on the same rationale
on the same guideline
on the same position
on the same charter
on the Republican principles
on the ethical principles
on the same regimen
on the established principles
on the same underlying
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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