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The phrase "first and second part" is correct and can be used in written English.
You can use it to refer to two distinct parts of something, as in this example: I divided my essay into two parts: the first and second part.
Exact(19)
The correlation coefficient between the first and second part of the scale was 0.80.
Fun upon Fun, or the first and second part of Miss Kitty Fisher's Merry thought.
62. Fun upon Fun, or the first and second part of Miss Kitty Fisher's Merry thought.
View the first and second part of the "Enduring Rifts" series on Chile.
As the scholar Richard Slotkin has noted, survey classes were organized chronologically, and the Civil War functioned as a dividing line between the first and second part.
A careful grid-independence study has been carried out in both the first and second part of the paper, and the influence of the spatial discretization of the convective fluxes has been discussed as well.
Similar(41)
In response, ICBP agreed to the first and second parts of Green Products' request, but it resisted the third part.
The next step for him is to narrow the gap between the first and second parts of the year.
The first and second parts are wholly the work of Aquinas; only the first 90 questions of the third part are his.
The first part was published in 1569; the second part appeared in 1578, when it was published with the first part; the third part was published with the first and second parts in 1589.
But unlike Waiting for Godot – in which, famously, nothing happens, twice – the first and second parts of Sondheim's musical are entirely different.
More suggestions(16)
first and second player
first and latter part
first and second parts
first and second contributed
first and second leaves
first and second portions
first and second nobody
first and second step
first and second degree
first and second order
first and preliminary part
first and second meeting
first and second book
first and third part
first and second year
first and second layer
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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