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"of the first type" is correct and usable in written English.
You can use this phrase to refer to something that belongs to a particular category or group. For example, "The painting was one of the first type of paintings created by the artist."
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Homer's Iliad is the first and greatest poetic account of the first type of war.
Musicians were understandably attracted to the fast pace and variety of the first type.
Soon after, he became one of the first type designers to predict that computers would both require and make possible digital typeface.
Examples of the first type include positioning systems for body support, control interfaces (e.g., keyboards, switches, and joysticks), and computers.
In any production run, the factory produces x1 of the first type and x2 of the second.
Bone of the first type begins in the embryonic skeleton with a cartilage model, which is gradually replaced by bone.
At that time the Venetian style still reigned, so that the opera is squarely of the first type.
Groups of the first type may have any number of members, sometimes up to 50 or more.
Examples of the first type of regulation are the federal clean-air and air- quality acts in the United States.
Reactions of the first type are most important for practical fusion energy production, whereas those of the second type are crucial to the initiation of star burning.
In devices of the first type, steam is condensed at below atmospheric pressure so as to gain the maximum amount of energy from it.
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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