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The phrase "the first kind of" is correct and usable in written English.
It can be used to categorize or specify a particular type or category among others.
Example: "This is the first kind of solution we have developed for this problem."
Alternatives: "the initial type of" or "the primary category of".
Exact(60)
The first kind of event is the Cosmetic Event.
The first kind of leak is the approved leak.
"That's the first kind of real empowering moment that Martin has as a father," he said.
And that might worry some people.On the first kind of question, the auspices are good.
Dehaene describes some fascinating and convincing evidence for the first kind of innateness.
The first kind of activity is "telic" — that is, directed toward an end, or telos.
These were the first kind of cakes I baked for my own children.
It was in relation to the first kind of anti-Semitism that Disraeli defined himself.
Most books that have food in them, including the classic nineteenth-century novels, have the first kind of food.
"In 40 years, this is the first kind of incident like this we've ever had," Mr. Carpenter said.
Integration by the arithmetic sequence (The first kind of solution).
More suggestions(16)
the first description of
the first model of
the first genera of
the first class of
the first genus of
the smartest kind of
the first species of
the commonest kind of
the largest kind of
the earliest kind of
the worst kind of
the truest kind of
the strongest kind of
the first sorts of
the first looks of
the first histories of
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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