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The phrase "applied the same principle" is correct and usable in written English.
You can use it when discussing the implementation of a consistent approach or method in different contexts or situations.
Example: "In her research, she applied the same principle to both experiments, ensuring that the results were comparable."
Alternatives: "utilized the same approach" or "employed the same method".
Exact(18)
Though the engine proved impractical, he later applied the same principle to develop a water meter.
After Alberto's birth, he applied the same principle to designing children's books and toys, then observed how his son responded to them.
Mr. Barbash applied the same principle when he joined efforts in the 1970s to stop the Long Island Lighting Company from completing the nuclear power plant at Shoreham.
And in 1982 the court applied the same principle to nullify a Seattle ballot initiative banning busing to desegregate the city's schools.
I think this would be a perfectly defensible position for her to take if only she applied the same principle when student unions invoke the NUS's no-platform policy.
After using this recipe successfully for potatoes, we later applied the same principle to a wide selection of other vegetables: carrots, beetroots (beets), turnips, radishes, or whatever we had.
Similar(39)
Mr. Domeny said he applied the same principles to business that he did to learning English.
Mr MacCready applied the same principles to his human-powered machines.
Since then we've applied the same principles to both, improving the products and services we offer as well as the business performance of each bank".
"I applied the same principles as one does to wine," he said.
Like Chengdu, Hangzhou applied the same principles, as Beijing has done, in implementing SRES.
More suggestions(2)
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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