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Some mathematical English translations and sentence usage are given (with extra points).
1. See the next page for tables involving other angles.

See the next page for a table of other angles.

Omit (may). You can see the next page.

A table plus s indicates that there are multiple tables.

2. Use the angle in quadrant I to represent the function of the angles in all quadrants.

The function of using angles in quadrant I to represent angles in all quadrants.

3. For the expansion of other quadrants, use the appropriate symbols given above.

Using the appropriate symbols given above, (these conclusions) can be extended to other quadrants

Extension plus s indicates that there are various extensions, such as extending to each quadrant.

Four ..... (formula in front) is a multivalued function of x and a set of univalent functions called branches. Similar other functions.

Is a multivalued function of x, where x is a set containing branches and branches are univalent functions.

5. For many purposes, a specific branch is needed. This is called the main branch, and the value of this branch is called the main value.

In most applications, a specific function is needed. This particular function is called the principal function, and the value of the principal function is called the principal value.

6. The solid part of the curve corresponds to the principal value.

The solid lines of these curves correspond to the principal values.

7. The following results apply to any triangle.

Support means: true for ... ...

8. Then the following results hold.

Hold: Created

The following results (theory) hold.

Subject+predicate structure

Assume that these quantities are arranged in a circle as shown in figure 1

We add the prefix co[ for complement] to the hypotenuse C. .....

Complement: refers to supplement.

9. In addition to the right angle C, the spherical triangle ABC has five parts. If arranged according to the other part shown in Figure 2, they will be ABA C B.

In addition to the right angle C, the spherical triangle ABC has five parts. If arranged according to Figure 2, these five parts are a b A c B respectively.