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The phrase "extend this principle" is correct and usable in written English.
You can use it when discussing the application or adaptation of a specific principle to a broader context or different situation.
Example: "In our research, we aim to extend this principle to other areas of study to see if it holds true across various disciplines."
Alternatives: "apply this principle" or "broaden this principle".
Exact(11)
However, today's judgment declined to extend this principle to disabled adults in a similar situation.
If government is so much more trustworthy than business, why shouldn't we extend this principle to food and shelter?
The government wants to extend this principle to offshore firms registered abroad, including in UK overseas territories such as the British Virgin Islands and other tax havens.
And we will extend this principle of transparency to every nook and cranny of politics and public life, because it's one of the quickest and easiest ways to transfer power to the powerless and prevent waste, exploitation and abuse.
We long ago inserted "intelligence" into objects in the form of thermostats and the like; the internet of everything will extend this principle exponentially, giving us unprecedented control over the objects that surround us.
We extend this principle to the 3D context, forming subarrays in the three dimensions of the recording space.
Similar(49)
The exhibition extends this principle.
The EU therefore has few qualms about extending this principle to America, even though it still seems to find American standards of food hygiene hard to swallow.
Several mathematicians improved and extended this principle by modifying the interpretation and pattern of the metric function for instance: cone metric spaces [5], G-metric spaces [6], partial metric spaces [7] and fuzzy metric spaces [8] etc.
Significant recent contributions can be found in Csáki and Gonchigdanzan [13], Chen and Lin [14], Tan et al. [15], and Tan and Peng [16], extending this principle by proving ASCLT for the maxima of a Gaussian sequence.
By extending this principle, it is possible to determine whether selecting for protection against a disease also selects for increased risk for a separate disease.
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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