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The phrase "both of the terms" is correct and usable in written English
It can be used when referring to two specific terms that have been previously mentioned or are known in the context. Example: "Both of the terms in the contract need to be agreed upon by both parties."
Exact(3)
If no PubMed document containing both of the terms is found, it suggests a possible new association between such concepts, a hypothesis for further exploration.
Of course, there are vague statements of identity – "Princeton is Princeton Borough" (Lewis 1988) – but the conclusion appears to follow that such vagueness is only possible when one or both of the terms flanking the sign of identity is an imprecise designator.
If participants answered in the negative, we encouraged them to suggest changes to one or both of the terms.
Similar(57)
In both meanings of the term, he's history.
Call it the "Good European," in both senses of the term.
She was concerned, in short, with sensation, in both meanings of the term.
"In other words, we're all under one roof, in both senses of the term.
Both meanings of the term are correct, and the earliest usages seem to favour a more local interpretation.
Mr. Pollini's view of musical history as perpetual revolution, with emphasis on both parts of the term, is in agreement with how he plays the piano.
Accurately configured but skeletal, the pistols have been turned from lethal weapons into sweet confections -- a disarming move in both senses of the term.
Both senses of the term occur in Spinoza's analysis of human perfection.
More suggestions(1)
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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