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The phrase "by the same reason" is correct and can be used in written English.
It is typically used to show that a conclusion or action is based on the same logic or reasoning as a previous one. Example: "I chose to study English literature in college, and by the same reason, I have decided to pursue a career in writing." In this sentence, the speaker is using "by the same reason" to explain that their decision to study English literature and their decision to pursue a writing career are based on the same logic or reasoning.
Exact(46)
But like you, I think we are all driven by the same reason.
It is proved by the same reason as the proof of Corollary 3.4.
by the same reason as the proof of Theorem 1.6, we can apply Lemma 3.7 to.
By the same reason, we conclude that there is no 3-dimensional integral manifold.
The same happens with the profiles ShortTC and FewBR, by the same reason.
However, most people are inclined to say that Jack and Jill's respective house purchases were motivated by the same reason.
Similar(14)
She then made things even worse by giving the same reason the Tories had given for making the same decision last year: that the threat of loyalist violence made the march the lesser of two evils.
We had a real vision of what we wanted the club to be, none of that stuff happened by happenstance, the same reason there wasn't a minimum.
They are motivated by the same reasons people have always gone to sea: money, adventure and escape.
It was about whether those around me asked the same questions as I did challenged the same things and were motivated by the same reasons.
Not everyone working in the sector will be motivated by the same reasons and this can be a challenge if you are expecting everyone to share your enthusiasm and outlook.
More suggestions(17)
by the same ground
by the same route
by the same law
by the same woman
by the same title
by the same degree
by the same family
by the same group
by the same margin
by the same legis
by the same algorithm
by the same security
by the same Creator
by the same person
by the same token
by the same philosophy
by the same idiot
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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